content stringlengths 5 1.05M |
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import firebase_admin
from firebase_admin import credentials, messaging
from firebase_admin.exceptions import FirebaseError
from secret import cred_cert
def test_firebase_call():
print('1')
if not firebase_admin._apps:
cred = credentials.Certificate(cred_cert)
default_app = firebase_admin.initialize_app(cred)
print('2')
body = 'Remind time 00:00'
n = messaging.Notification(title = 'test_firebase_call', body = body, image = None)
priority = 'normal'
myicon = 'https://rusel.by/static/rok/img/test-192.png'
mybadge = 'https://rusel.by/static/rok/img/test-72.png'
click_action = 'https://rusel.by/todo/99999/'
an = messaging.AndroidNotification(title = 'test_firebase_call', body = body, icon = myicon, color = None, sound = None, tag = None, click_action = click_action, body_loc_key = None, \
body_loc_args = None, title_loc_key = None, title_loc_args = None, channel_id = None, image = None, ticker = None, sticky = None, \
event_timestamp = None, local_only = None, priority = None, vibrate_timings_millis = None, default_vibrate_timings = None, \
default_sound = None, light_settings = None, default_light_settings = None, visibility = None, notification_count = None)
añ = messaging.AndroidConfig(collapse_key = None, priority = priority, ttl = None, restricted_package_name = None, data = None, notification = an, fcm_options = None)
actions = []
a1 = messaging.WebpushNotificationAction('postpone', 'Postpone', icon = 'https://rusel.by/static/todo/icon/remind-today.png')
a2 = messaging.WebpushNotificationAction('done', 'Done', icon = 'https://rusel.by/static/rok/icon/delete.png')
actions.append(a1)
actions.append(a2)
print('3')
#wn = messaging.WebpushNotification(title = task.name, body = body, icon = icon, actions = actions, badge = None, data = None, direction = None, image = None, language = None, renotify = True, require_interaction = True, silent = False, tag = None, timestamp_millis = None, vibrate = None, custom_data = None)
wn = messaging.WebpushNotification(title = 'test_firebase_call', body = body, icon = myicon, badge = mybadge, actions = actions, tag = '99999', custom_data = {"click_action": click_action})
wo = messaging.WebpushFCMOptions(click_action)
wc = messaging.WebpushConfig(headers = None, data = None, notification = wn, fcm_options = None)
tokens = []
tokens.append('dq6oUJNrQ2IYcm3mVtzfw8:APA91bE_3q9CdIAMWw6Blh0uGmLve5dv_AeHY4kJec6tGM34Vw3wMN6WIEZveI60Yl0neNeeSzmD1zwcvuC0A49Ht7t90mHxD47jE8duyQX0090qRflS7hVo0lm-qJ_wLJsJ59_nJFtQ')
print('4')
mm = messaging.MulticastMessage(tokens = tokens, data = None, notification = n, android = None, webpush = wc, apns = None, fcm_options = None)
print('5')
r = messaging.send_multicast(mm, dry_run = False, app = None)
print('6')
ret_resp = '[' + str(len(r.responses)) + ']: '
npp = 0
for z in r.responses:
if (len(ret_resp) > 0):
ret_resp += ', '
if z.success:
ret_resp += '1'
else:
ret_resp += '0 ' + z.exception.code
if (z.exception.code == 'NOT_FOUND'):
ss[npp].delete()
npp += 1
if z.message_id:
ret_resp += ':' + z.message_id
if __name__ == '__main__':
test_firebase_call()
|
import numpy as np
from scipy.constants import c as c_light, e as qe, m_p
from scipy.signal import hilbert
from scipy.stats import linregress
from PyHEADTAIL.feedback.transverse_damper import TransverseDamper
from PyHEADTAIL.machines.synchrotron import Synchrotron
def test_damping_time():
n_attempts = 5
n_turns = 800
macroparticlenumber = int(1e5)
# Beam and machine parameters
intensity = 2e11
epsn_x = 2e-6 # normalised horizontal emittance
epsn_y = 2e-6 # normalised vertical emittance
p0_eVperc = 6.5e12
p0 = p0_eVperc * qe / c_light
beta_x = 92.7
beta_y = 93.2
Q_x = 64.31
Q_y = 59.32
alpha_momentum = 3.225e-4
h_RF = 35640
V_RF = 12.0e6
circumference = 26658.883199999
# Create machine
machine = Synchrotron(optics_mode='smooth', circumference=circumference,
n_segments=1, beta_x=beta_x, beta_y=beta_y,
D_x=0.0, D_y=0.0, accQ_x=Q_x, accQ_y=Q_y,
alpha_mom_compaction=alpha_momentum,
longitudinal_mode='non-linear', h_RF=h_RF, V_RF=V_RF,
dphi_RF=0, p_increment=0.0,
p0=p0, charge=qe, mass=m_p)
sigma_z = 1e-9 * machine.beta * c_light / 4. # RMS bunch length in meters
# Damper
damping_time = 200 # [turns]
damper = TransverseDamper(dampingrate_x=damping_time,
dampingrate_y=damping_time)
machine.one_turn_map.append(damper)
# Loop over attempts
i_attempt = 0
while i_attempt < n_attempts:
print(f"Attempt {i_attempt+1}:")
# Create beam
bunch = machine.generate_6D_Gaussian_bunch_matched(
n_macroparticles=macroparticlenumber,
intensity=intensity,
epsn_x=epsn_x,
epsn_y=epsn_y,
sigma_z=sigma_z,
)
# Kick beam
kick_in_sigmas = 0.75
bunch.x += kick_in_sigmas * bunch.sigma_x()
bunch.x += kick_in_sigmas * bunch.sigma_y()
# Create arrays for saving
x = np.zeros(n_turns, dtype=float)
y = np.zeros(n_turns, dtype=float)
# Tracking loop
for i in range(n_turns):
for m in machine.one_turn_map:
m.track(bunch)
x[i], y[i] = bunch.mean_x(), bunch.mean_y()
# Check results
turns = range(n_turns)
iMin = 5
iMax = n_turns - 5
ampl_x = np.abs(hilbert(x))
b_x, a, r, p, stderr = linregress(turns[iMin:iMax],
np.log(ampl_x[iMin:iMax]))
print(f"Damping time x {-1/b_x:.0F} [turns]")
ampl_y = np.abs(hilbert(y))
b_y, a, r, p, stderr = linregress(turns[iMin:iMax],
np.log(ampl_y[iMin:iMax]))
print(f"Damping time y {-1/b_y:.0F} [turns]")
# assert np.isclose(-1/b_x, damping_time, rtol=2e-2), \
# "Horizontal damping time doesn't match"
# assert np.isclose(-1/b_y, damping_time, rtol=2e-2), \
# "Vertical damping time doesn't match"
check_x = np.isclose(-1/b_x, damping_time, rtol=2e-2)
check_y = np.isclose(-1/b_y, damping_time, rtol=2e-2)
assert check_x or i_attempt < n_attempts-1, \
f"After {n_attempts} attempts horizontal damping time doesn't match"
assert check_y or i_attempt < n_attempts-1, \
f"After {n_attempts} attempts vertical damping time doesn't match"
if check_x and check_y:
print(f"Passed on {i_attempt + 1}. attempt.")
break
i_attempt += 1
def test_damping_time_xy():
n_attempts = 5
n_turns = 800
macroparticlenumber = int(1e5)
# Beam and machine parameters
intensity = 2e11
epsn_x = 2e-6 # normalised horizontal emittance
epsn_y = 2e-6 # normalised vertical emittance
p0_eVperc = 6.5e12
p0 = p0_eVperc * qe / c_light
beta_x = 92.7
beta_y = 93.2
Q_x = 64.31
Q_y = 59.32
alpha_momentum = 3.225e-4
h_RF = 35640
V_RF = 12.0e6
circumference = 26658.883199999
# Create machine
machine = Synchrotron(optics_mode='smooth', circumference=circumference,
n_segments=1, beta_x=beta_x, beta_y=beta_y,
D_x=0.0, D_y=0.0, accQ_x=Q_x, accQ_y=Q_y,
alpha_mom_compaction=alpha_momentum,
longitudinal_mode='non-linear', h_RF=h_RF, V_RF=V_RF,
dphi_RF=0, p_increment=0.0,
p0=p0, charge=qe, mass=m_p)
sigma_z = 1e-9 * machine.beta * c_light / 4. # RMS bunch length in meters
# Damper
damping_time = 200 # [turns]
damper_x = TransverseDamper(dampingrate_x=damping_time,
dampingrate_y=0, phase=87,
local_beta_function=93.)
damper_y = TransverseDamper(dampingrate_x=0,
dampingrate_y=damping_time, phase=93,
local_beta_function=93.)
machine.one_turn_map.append(damper_x)
machine.one_turn_map.append(damper_y)
# Loop over attempts
i_attempt = 0
while i_attempt < n_attempts:
print(f"Attempt {i_attempt+1}")
# Create beam
bunch = machine.generate_6D_Gaussian_bunch_matched(
n_macroparticles=macroparticlenumber,
intensity=intensity,
epsn_x=epsn_x,
epsn_y=epsn_y,
sigma_z=sigma_z,
)
# Kick beam
kick_in_sigmas = 0.75
bunch.x += kick_in_sigmas * bunch.sigma_x()
bunch.x += kick_in_sigmas * bunch.sigma_y()
# Create arrays for saving
x = np.zeros(n_turns, dtype=float)
y = np.zeros(n_turns, dtype=float)
# Tracking loop
for i in range(n_turns):
for m in machine.one_turn_map:
m.track(bunch)
x[i], y[i] = bunch.mean_x(), bunch.mean_y()
# Check results
turns = range(n_turns)
iMin = 5
iMax = damping_time - 5
ampl_x = np.abs(hilbert(x))
b_x, a, r, p, stderr = linregress(turns[iMin:iMax],
np.log(ampl_x[iMin:iMax]))
print(f"Damping time x {-1/b_x:.0F} [turns]")
ampl_y = np.abs(hilbert(y))
b_y, a, r, p, stderr = linregress(turns[iMin:iMax],
np.log(ampl_y[iMin:iMax]))
print(f"Damping time y {-1/b_y:.0F} [turns]")
# assert np.isclose(-1/b_x, damping_time, rtol=2e-2), \
# "Horizontal damping time doesn't match"
# assert np.isclose(-1/b_y, damping_time, rtol=2e-2), \
# "Vertical damping time doesn't match"
check_x = np.isclose(-1/b_x, damping_time, rtol=2e-2)
check_y = np.isclose(-1/b_y, damping_time, rtol=2e-2)
assert check_x or i_attempt < n_attempts-1, \
f"After {n_attempts} attempts horizontal damping time doesn't match"
assert check_y or i_attempt < n_attempts-1, \
f"After {n_attempts} attempts vertical damping time doesn't match"
if check_x and check_y:
print(f"Passed on {i_attempt + 1}. attempt.")
break
i_attempt += 1
|
"""Top-level package for chess_clock."""
__author__ = """Musharraf Omer"""
__email__ = 'ibnomer2011@hotmail.com'
__version__ = '0.1.0'
|
# -*- coding: utf-8 -*-
"""
Created on Thu Dec 2 11:43:37 2021
@author: Chai Wah Wu
Python functions to generate The On-Line Encyclopedia of Integer Sequences (OEIS) sequences
Requires python >= 3.8
Installation: pip install OEISsequences
After installation, `from oeis_sequences import OEISsequences` will import all the functions accessible via `OEISsequences.Axxxxxx`.
Alternatively, invidividual functions can be imported as `from oeis_sequences.OEISsequences import Axxxxxx`.
For each sequence, there are 3 different kinds of functions:
1. Functions named `Axxxxxx`: Axxxxxx(n) returns the *n*-th term of OEIS sequence Axxxxxx.
2. Functions named `Axxxxxx_T`: returns T(n,k) for OEIS sequences where the natural definition is a 2D table T.
3. Functions named `Axxxxxx_gen`: Axxxxxx_gen() returns a generator of OEIS sequence Axxxxxx.
The function `Axxxxxx` is best used to compute a single term. The generator `Axxxxxx_gen` is typically defined for sequences where terms are best generated sequentially and is best used when computing a sequence of consecutive terms.
For the generator, we can for example use `list(islice(Axxxxxx_gen(),10))` to return the first 10 terms of sequence Axxxxxx
Alternatively, setting `gen = Axxxxxx_gen()` and using `next(gen)` returns the next term of the sequence.
Given `Axxxxxx_gen`, one can define a function `Axxxxxx` as:
def Axxxxxx(n,offset=1): return next(islice(Axxxxxx_gen(),n-offset,None))
where a(offset) is the first term returned by the generator. This value of offset is the same as the offset parameter in the OEIS database.
Some functions `Axxxxxx_gen` contain an optional keyword `startvalue` that returns a generator of terms that are larger than or equal to `startvalue`.
For some sequences, e.g. `A269483`, both type of functions `Axxxxxx` and `Axxxxxx_gen` are provided.
Examples:
from oeis_sequences.OEISsequences import A131546
print(A131546(5))
>> 721
from itertools import islice
from oeis_sequences.OEISsequences import A153695_gen
print(list(islice(A153695_gen(),10)))
>> [1, 2, 3, 4, 5, 6, 13, 17, 413, 555]
from oeis_sequences.OEISsequences import A235811_gen
print(list(islice(A235811_gen(startvalue=1475),10)))
>> [1475, 1484, 1531, 1706, 1721, 1733, 1818, 1844, 1895, 1903]
The module also includes some utility functions for exploring integer sequences in OEIS such as palindrome generator,
Boustrophedon transform, run length transform, lunar arithmetic, etc.
"""
from __future__ import print_function, division
import sys, bisect, re
from functools import lru_cache, reduce
from itertools import (
islice,
count,
product,
permutations,
takewhile,
accumulate,
combinations_with_replacement,
combinations,
repeat,
groupby,
chain,
starmap,
)
from fractions import Fraction
from collections import Counter, deque
from math import factorial, floor, comb, prod, isqrt
from operator import mul, xor, add, or_
from operator import sub as operator_sub
from re import finditer, split, sub
from statistics import pvariance
from sympy.core.numbers import igcdex
from sympy import (
factorint,
divisors,
integer_nthroot,
divisor_sigma,
nextprime,
Matrix,
divisor_count,
isprime,
prime,
totient,
sympify,
primerange,
primepi,
composite,
compositepi,
factorial2,
prevprime,
primefactors,
harmonic,
multiplicity,
n_order,
primorial,
sqrt,
bernoulli,
ff,
rf,
sin,
cos,
tan,
fibonacci,
lucas,
pi,
hyperexpand,
expand,
Poly,
hermite,
mod_inverse,
EulerGamma,
digamma,
discrete_log,
S,
catalan,
npartitions,
ceiling,
log,
simplify,
)
from sympy.functions import hyper, partition, euler
from sympy.ntheory import (
mobius,
jacobi_symbol,
legendre_symbol,
sqrt_mod,
multinomial_coefficients,
)
from sympy.ntheory.factor_ import (
digits as sympydigits,
udivisor_sigma,
sieve,
reduced_totient,
core as numbercore,
antidivisors,
udivisors,
antidivisor_count,
)
from sympy.combinatorics.partitions import IntegerPartition
from sympy.utilities.iterables import (
partitions,
multiset_permutations,
multiset_combinations,
multiset_partitions,
)
from sympy.functions.combinatorial.numbers import stirling, bell
from sympy.ntheory.continued_fraction import (
continued_fraction,
continued_fraction_periodic,
continued_fraction_reduce,
)
from sympy.ntheory.modular import crt
from sympy.ntheory.residue_ntheory import nthroot_mod
from sympy.combinatorics.subsets import Subset
from sympy.solvers.diophantine import diophantine
from sympy.solvers.diophantine.diophantine import diop_quadratic, diop_DN
from sympy.abc import x as symbolx, y as symboly
from gmpy2 import (
mpz,
fac,
popcount,
is_prime,
is_square,
next_prime,
c_divmod,
lucas2,
fib,
fib2,
isqrt_rem,
iroot_rem,
is_power,
digits as gmpy2digits,
)
from num2words import num2words
from unidecode import unidecode
if sys.version_info < (3, 9):
from sympy import lcm as sympylcm, gcd as sympygcd
def gcd(*x):
r = x[0]
for y in x[1:]:
r = sympygcd(r, y)
return r
def lcm(*x):
r = x[0]
for y in x[1:]:
r = sympylcm(r, y)
return r
else:
from math import lcm, gcd
""" Utility functions """
def is_pal(n, b=10):
"""check if n is a palindrome in base b"""
return (s := sympydigits(n, b)[1:]) == s[::-1]
def is_cubefree_string(s):
"""check if s is a cubefree string, i.e. there is no substring of the form ttt"""
l = len(s)
for i in range(l - 2):
for j in range(1, (l - i) // 3 + 1):
if s[i : i + 2 * j] == s[i + j : i + 3 * j]:
return False
return True
def pal10_gen():
"""generator of palindromes in base 10"""
yield 0
for x in count(1):
for y in range(10 ** (x - 1), 10**x):
s = str(y)
yield int(s + s[-2::-1])
for y in range(10 ** (x - 1), 10**x):
s = str(y)
yield int(s + s[::-1])
def pal_gen(b=10):
"""generator of palindromes in base b"""
yield 0
x = 1
while True:
n = b ** (x - 1)
n2 = n * b
for y in range(n, n2): # odd-length
k, m = y // b, 0
while k >= b:
k, r = divmod(k, b)
m = b * m + r
yield y * n + b * m + k
for y in range(n, n2): # even length
k, m = y, 0
while k >= b:
k, r = divmod(k, b)
m = b * m + r
yield y * n2 + b * m + k
x += 1
def palbase_gen(b=10):
"""generator of palindromes in base b <=10 written in base b"""
yield 0
for x in count(1):
for y in range(b ** (x - 1), b**x):
s = gmpy2digits(y, b)
yield int(s + s[-2::-1])
for y in range(b ** (x - 1), b**x):
s = gmpy2digits(y, b)
yield int(s + s[::-1])
def pal_odd_gen(l, b=10):
"""generator of odd-length palindromes in base b of length <= 2*l"""
if l > 0:
yield 0
for x in range(1, l + 1):
n = b ** (x - 1)
n2 = n * b
for y in range(n, n2):
k, m = y // b, 0
while k >= b:
k, r = divmod(k, b)
m = b * m + r
yield y * n + b * m + k
def pal10_odd_range_gen(m=1):
"""generator of odd-length palindromes in base 10 of length at least m"""
if m == 1:
yield 0
for x in count(m // 2 + 1):
n = 10 ** (x - 1)
for y in range(n, n * 10):
s = str(y)
yield int(s + s[-2::-1])
def multiset_perm_count(x):
"""count the number of permutations in a multiset (from a list or tuple)"""
return factorial(len(x)) // prod(factorial(d) for d in Counter(x).values())
def intpartitiongen(n, m):
"""generator of partition of n into m decimal digits, return as list of strings"""
return (
"".join(str(d) for d in IntegerPartition(p).partition + [0] * (m - s))
for s, p in partitions(n, k=9, m=m, size=True)
)
@lru_cache(maxsize=None)
def intpartition(n, m):
"""partition of n into m decimal digits, return as list of strings"""
return tuple(intpartitiongen(n, m))
def partitionpairs(xlist):
"""generator of all partitions into pairs and at most 1 singleton, returning the sums of the pairs"""
if len(xlist) <= 2:
yield [sum(xlist)]
else:
m = len(xlist)
for i in range(m - 1):
for j in range(i + 1, m):
rem = xlist[:i] + xlist[i + 1 : j] + xlist[j + 1 :]
y = [xlist[i] + xlist[j]]
for d in partitionpairs(rem):
yield y + d
def integerlog(n, b):
"""computes largest integer k>=0 such that b^k <= n"""
kmin, kmax = 0, 1
while b**kmax <= n:
kmax *= 2
while True:
kmid = (kmax + kmin) // 2
if b**kmid > n:
kmax = kmid
else:
kmin = kmid
if kmax - kmin <= 1:
break
return kmin
def ispandigital(m, n):
"""return True iff m is pandigital in base n"""
s = set()
while m > 0:
m, b = divmod(m, n)
if b in s:
return False
s.add(b)
return True
def ispandigital0(m, n):
"""return (True, s) if m is pandigital in base n and (False, False) otherwise where s is true iff m has a zero digit"""
s = set()
z = False
while m > 0:
m, b = divmod(m, n)
if b in s:
return False, False
if b == 0:
z = True
s.add(b)
return True, z
def intbase(dlist, b=10):
"""convert list of digits in base b to integer"""
y = 0
for d in dlist:
y = y * b + d
return y
def is_emirp(n, b=10):
"""check if n is an emirp in base b"""
x, y = n, 0
while x >= b:
x, r = divmod(x, b)
y = y * b + r
y = y * b + x
return n != y and isprime(y)
def antidivisor_sigma(n):
"""sum of antidivisors of n"""
return (
sum(2 * d for d in divisors(n, generator=True) if n > 2 * d and n % (2 * d))
+ sum(d for d in divisors(2 * n - 1, generator=True) if n > d >= 2 and n % d)
+ sum(d for d in divisors(2 * n + 1, generator=True) if n > d >= 2 and n % d)
)
def divisor_prod(n):
"""product of divisors of n"""
d = divisor_count(n)
return isqrt(n) ** d if d % 2 else n ** (d // 2)
def divisor_sigma_mod(n, m):
"""computes divisor_sigma(n) mod m"""
y = 1
for p, e in factorint(n).items():
y = (y * (p ** (e + 1) - 1) // (p - 1)) % m
return y
def reversedigits(n, b=10):
"""reverse digits of n in base b"""
x, y = n, 0
while x >= b:
x, r = divmod(x, b)
y = b * y + r
return b * y + x
@lru_cache(maxsize=None)
def divisor_tuple(n):
"""cached unordered tuple of divisors"""
return tuple(divisors(n, generator=True))
def RLT(n, f):
"""run length transform of a function f"""
return prod(f(len(d)) for d in split("0+", bin(n)[2:]) if d != "") if n > 0 else 1
def repeating_decimals_expr(f, digits_only=False):
"""returns repeating decimals of Fraction f as the string aaa.bbb[ccc].
returns only digits if digits_only=True.
"""
a, b = f.as_integer_ratio()
m2, m5 = multiplicity(2, b), multiplicity(5, b)
r = max(m2, m5)
k, m = 10**r, 10 ** (t := n_order(10, b // 2**m2 // 5**m5)) - 1
c = k * a // b
s = str(c).zfill(r)
if digits_only:
return s + str(m * k * a // b - c * m).zfill(t)
else:
w = len(s) - r
return s[:w] + "." + s[w:] + "[" + str(m * k * a // b - c * m).zfill(t) + "]"
def Boustrophedon_transform(x):
"""Boustrophedon transform of the iterable x
returns generator"""
blist = tuple()
for m in x:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
def inverse_Boustrophedon_transform(x):
"""inverse Boustrophedon transform of the iterable x
returns generator"""
blist = tuple()
for m in x:
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=m))
)[-1]
""" Lunar arithmetic """
def lunar_add(n, m):
"""lunar addition"""
sn, sm = str(n), str(m)
l = max(len(sn), len(sm))
return int("".join(max(i, j) for i, j in zip(sn.rjust(l, "0"), sm.rjust(l, "0"))))
def lunar_mul(n, m):
"""lunar multiplication"""
sn, sm, y = str(n), str(m), 0
for i in range(len(sm)):
c = sm[-i - 1]
y = lunar_add(y, int("".join(min(j, c) for j in sn)) * 10**i)
return y
""" """
""" List of OEIS sequences """
def A349804(n):
return int((lambda x: x + x[::-1])("".join(str(d) for d in range(1, n + 1))))
def A349805(n):
return int((lambda x: x + x[::-1])("".join(str(d) for d in range(1, n + 1)))) // 11
def A173426(n):
return int(
"".join(str(d) for d in range(1, n + 1))
+ "".join(str(d) for d in range(n - 1, 0, -1))
)
def A349724(): # generator of terms
for k in count(1):
if (
not k
* (k + 1)
// 2
% prod(p ** (e - 1) * ((p - 1) * e + p) for p, e in factorint(k).items())
):
yield k
def A018804(n):
return prod(p ** (e - 1) * ((p - 1) * e + p) for p, e in factorint(n).items())
def A349711(n):
f = factorint(n)
plist, m = list(f.keys()), sum(f[p] * p for p in f)
return sum(
(lambda x: x * (m - x))(sum(d[i] * p for i, p in enumerate(plist)))
for d in product(*(list(range(f[p] + 1)) for p in plist))
)
def A349712(n):
f = factorint(n)
plist = list(f.keys())
return sum(
sum(int(d[i] > 0) * p for i, p in enumerate(plist))
* sum(int(d[i] < f[p]) * p for i, p in enumerate(plist))
for d in product(*(list(range(f[p] + 1)) for p in plist))
)
def A348169_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
for d in divisors(n, generator=False):
x, x2 = 1, 1
while 3 * x2 <= d:
y, y2 = x, x2
z2 = d - x2 - y2
while z2 >= y2:
z, w = integer_nthroot(z2, 2)
if w:
A = n // d
B, u = divmod(n, x * (y + z) + y * z)
if u == 0 and gcd(A, B) == 1:
yield n
break
y += 1
y2 += 2 * y - 1
z2 -= 2 * y - 1
else:
x += 1
x2 += 2 * x - 1
continue
break
else:
continue
break
def A349680(n):
return n + (n - 1) * divisor_sigma(n, 0) - divisor_sigma(n, 1)
def A349643(n):
plist, clist = [2], [1]
for i in range(1, n + 1):
plist.append(nextprime(plist[-1]))
clist.append((-1) ** i * comb(n, i))
while True:
if sum(clist[i] * plist[i] for i in range(n + 1)) == 0:
return plist[0]
plist = plist[1:] + [nextprime(plist[-1])]
def A349544helper_(k, n):
if k == 0 and n == 0:
return (x for x in (1,))
if k < n:
return (y * 3 for y in A349544helper_(k, n - 1))
return (abs(x + y) for x in A349544helper_(k - 1, n) for y in (2**n, -(2**n)))
def A349544(n):
return min(A349544helper_(n, n))
def A348183(n):
return Matrix(n, n, [pow(i + j, 2, n) for i in range(n) for j in range(n)]).det()
def A348226(n):
"""code assumes n <= 63 or n is prime"""
if is_prime(n):
return 2
if n > 63:
return "Error: n <= 63 or n is prime"
p = 2
while True:
for i in range(n - 1, 1, -1):
s = gmpy2digits(p, i)
if not is_prime(int(s, n)):
break
else:
return p
p = next_prime(p)
def A349529(n):
return len(
list(
filter(
lambda x: x == 1,
Counter(
"".join(d)
for d in permutations(bin(i)[2:] for i in range(1, n + 1))
).values(),
)
)
)
def A066640_gen():
return filter(
lambda n: all(
set(str(m)) <= {"1", "3", "5", "7", "9"}
for m in divisors(n, generator=True)
),
count(1, 2),
)
def A014261_gen():
return filter(lambda n: set(str(n)) <= {"1", "3", "5", "7", "9"}, count(1, 2))
def A117960_gen():
return filter(
lambda n: set(str(n)) <= {"1", "3", "5", "7", "9"},
(m * (m + 1) // 2 for m in count(0)),
)
def A349243_gen(startvalue=0):
return filter(
lambda n: set(str(n * (n + 1) // 2)) <= {"1", "3", "5", "7", "9"},
count(max(startvalue, 0)),
)
def A348162_gen(): # generator of terms
s, n, m = "0", 1, 0
while True:
yield m
n, m = n * 2, int(s, 4) + int(("02" * n)[: len(s)], 4)
s = format(m, "0" + str(n) + "b")
def A349360(n):
m = divisor_count(n)
return m * (m - n) + n * (n + 1) // 2
def A349460_gen():
return filter(lambda n: set(str(n)) <= {"0", "2", "4"}, (n * n for n in count(0)))
def A342975_gen():
return filter(lambda n: set(str(n)) <= {"0", "1", "3"}, (n**3 for n in count(0)))
def A050251(n):
return (
4 * n if n <= 1 else 1 + sum(1 for i in pal_odd_gen((n + 1) // 2) if isprime(i))
)
def A229629_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s, sn = str(n**n), str(n)
l, ln = len(s), len(sn)
if (ln - l) % 2 == 0 and s[l // 2 - ln // 2 : l // 2 + (ln + 1) // 2] == sn:
yield n
def A347113_gen(): # generator of terms
j, nset, m = 2, {1}, 2
yield 1
while True:
k = m
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
yield k
j = k + 1
nset.add(k)
while m in nset:
m += 1
def A347313(n):
p, gen = prime(n), A347113_gen()
for i in count(1):
q = next(gen)
if p == q:
return i
def A179993_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
if all(
isprime(m // a - a) for a in takewhile(lambda x: x * x <= m, divisors(m))
):
yield m
def A349327_gen(): # generator of terms
n = 2
while True:
if isprime(n**2 - 2) and isprime(2 * n**2 - 1):
yield n
n = nextprime(n)
def A348784_gen(): # generator of terms
i = 1
for m in A347113_gen():
if isprime(m):
yield i
i += 1
def A348158(n):
return sum(set(map(totient, divisors(n, generator=True))))
def A348213(n):
c, k = 0, n
m = A348158(k)
while m != k:
k, m = m, A348158(m)
c += 1
return c
def A003434(n):
c, m = 0, n
while m > 1:
c += 1
m = totient(m)
return c
def A013588(n):
s, k = set(Matrix(n, n, p).det() for p in product([0, 1], repeat=n**2)), 1
while k in s:
k += 1
return k
def iteratedphi(n):
m = n
while m > 1:
m = totient(m)
yield m
def A092694(n):
return prod(iteratedphi(n))
def A092693(n):
return sum(iteratedphi(n))
def A254007(n):
return (
1
if n == 0
else len(
set(tuple(sorted(accumulate(d))) for d in product((-1, 1), repeat=n - 1))
)
)
def A348780(n):
return sum(islice(A347113_gen(), n))
def A343878(n):
k, c = 0, dict()
while True:
m, r = 0, 1
while r > 0:
k += 1
r = c.get(m, 0)
if n == r:
return k
c[r] = c.get(r, 0) + 1
m += 1
def A348781(n):
k, s, c = 0, 0, dict()
while True:
m, r = 0, 1
while r > 0:
k += 1
if k > n:
return s
r = c.get(m, 0)
s += r
c[r] = c.get(r, 0) + 1
m += 1
def A172500(n):
return sympify("0.[" + str(n) + "]").p
def A172502(n):
return sympify("0.[" + str(n) + "]").q
def A348870(n):
return (lambda m, r: r.p if m % 2 else r.q)(
n, sympify("0.[" + str((n + 1) // 2) + "]")
)
def A339665(n):
ds = tuple(divisors(n, generator=True))
return sum(
sum(1 for d in combinations(ds, i) if n * i % sum(d) == 0)
for i in range(1, len(ds) + 1)
)
def A339453(n):
m = lcm(*range(2, n + 1))
return sum(
1
for i in range(1, n + 1)
for d in combinations((m // i for i in range(1, n + 1)), i)
if m * i % sum(d) == 0
)
def A349148(n):
k = lcm(*range(2, n + 1))
return sum(
1
for d in combinations_with_replacement((k // d for d in range(1, n + 1)), n)
if sum(d) % k == 0
)
def A349215(n):
fs = factorint(n)
return sum(a - 1 for a in fs.keys()) + prod(1 + d for d in fs.values())
def A349214(n):
p = list(primerange(2, n + 1))
return n - len(p) + sum(p)
@lru_cache(maxsize=None)
def A339508(n):
nlist = [i for i in range(2, n) if i % 10 != 0]
if n == 0 or n == 1:
return 1
c = A339508(n - 1)
if n % 10 != 0:
sn = str(n)
if sn == sn[::-1]:
c += 1
for i in range(1, len(nlist) + 1):
for d in combinations(nlist, i):
s = str(prod(d) * n)
if s == s[::-1]:
c += 1
return c
@lru_cache(maxsize=None)
def A339484(n):
return (
1
if n == 1
else A339484(n - 1)
+ sum(
sum(d) + n == (i + 1) ** 2
for i in range(1, n)
for d in combinations(range(1, n), i)
)
)
def A348516(n):
k, s = 1, gmpy2digits(n, 3).rstrip("0")
if s == "1" or s == "":
return 1 - len(s)
m = int(s, 3)
mk = m
while s.count("1") != s.count("2"):
k += 1
mk *= m
s = gmpy2digits(mk, 3)
return k
def A349179_gen(): # generator of terms
c = 0
for i in count(1):
if (m := A339665(i)) > c:
yield i
c = m
def A349145(n):
return sum(
1
for d in product(range(1, n + 1), repeat=n)
if sum(Fraction(i + 1, j) for i, j in enumerate(d)).denominator == 1
)
def A349146(n):
k = lcm(*range(2, n + 1))
dlist = tuple(k // d for d in range(1, n + 1))
return sum(
multiset_perm_count(d)
for d in combinations_with_replacement(range(1, n + 1), n)
if sum(dlist[e - 1] for e in d) % k == 0
)
def A348895(n):
l, c, nmax, k = 9 * n, 0, 0, 10 ** (n - 1)
while l > c:
for p in intpartition(l, n):
for q in multiset_permutations(p):
w = int("".join(q))
if w >= k:
wr = w % l
if wr > c:
c = wr
nmax = w
if wr == c and nmax < w:
nmax = w
l -= 1
return nmax
def A348894(n):
l, c, nmin, k = 9 * n, 0, 10**n - 1, 10 ** (n - 1)
while l > c:
for p in intpartition(l, n):
for q in multiset_permutations(p):
w = int("".join(q))
if w >= k:
wr = w % l
if wr > c:
c = wr
nmin = w
if wr == c and nmin > w:
nmin = w
l -= 1
return nmin
def A348730(n):
l, c, k = 9 * n, 0, 10 ** (n - 1)
while l - 1 > c:
c = max(
c,
max(
s % l
for s in (
int("".join(q))
for p in intpartition(l, n)
for q in multiset_permutations(p)
)
if s >= k
),
)
l -= 1
return c
def A348706(n):
return int(gmpy2digits(n, 3).replace("0", ""), 3)
def A348651(n):
return popcount(fac(fac(n)))
def A348658_gen(startvalue=1): # generator of terms
for k in count(max(startvalue, 1)):
a, b = divisor_sigma(k), divisor_sigma(k, 0) * k
c = gcd(a, b)
n1, n2 = 5 * (a // c) ** 2 - 4, 5 * (b // c) ** 2 - 4
if (integer_nthroot(n1, 2)[1] or integer_nthroot(n1 + 8, 2)[1]) and (
integer_nthroot(n2, 2)[1] or integer_nthroot(n2 + 8, 2)[1]
):
yield k
def A108861_gen(): # generator of terms
k2, kf = 1, 1
for k in count(1):
k2 *= 2
kf *= k
if not sum(int(d) for d in str(k2 * kf)) % k:
yield k
def A244060(n):
return sum(int(d) for d in str(factorial(2**n)))
def A008906(n):
return len(str(factorial(n)).rstrip("0"))
def A348446_gen(): # generator of terms. Greedy algorithm.
a = 1
c, b = Counter(), 1
while True:
k, kb = 1, b
while c[kb] >= kb:
k += 1
kb += b
c[kb] += 1
b = k
a2 = k
yield a - a2
k, kb = 1, b
while c[kb] >= kb:
k += 1
kb += b
c[kb] += 1
b = k
a = k
def A348441_gen(): # generator of terms
yield 1
c, p, a = 1, {1}, 1
for i in count(3):
n, na = 1, a
while na in p:
n += 1
na += a
p.add(na)
a = n
if c < n:
c = n
yield i
def A348247(n):
c, b, p = Counter(), 1, prime(n)
for i in count(1):
k, kb = 1, b
while c[kb] >= kb:
k += 1
kb += b
if kb == p:
return i
c[kb] += 1
b = k
def A348353_gen(): # generator of terms.
p, q, r = 2, 3, 5
while True:
if isprime(p * p + q + r) and isprime(p + q * q + r) and isprime(p + q + r * r):
yield p
p, q, r = q, r, nextprime(r)
def A307730_gen(): # generator of terms. Greedy algorithm.
c, b = Counter(), 1
while True:
k, kb = 1, b
while c[kb] >= kb:
k += 1
kb += b
c[kb] += 1
b = k
yield kb
def A348442_gen(): # generator of terms
yield 1
c, p, a = 1, {1}, 1
while True:
n, na = 1, a
while na in p:
n += 1
na += a
p.add(na)
a = n
if c < na:
c = na
yield c
def A348443_gen(): # generator of terms
yield 1
c, p, a = 1, {1}, 1
for i in count(2):
n, na = 1, a
while na in p:
n += 1
na += a
p.add(na)
a = n
if c < na:
c = na
yield i
def A348440_gen(): # generator of terms
yield 1
c, p, a = 1, {1}, 1
while True:
n, na = 1, a
while na in p:
n += 1
na += a
p.add(na)
a = n
if c < n:
c = n
yield c
def A088177_gen(): # generator of terms
yield 1
yield 1
p, a = {1}, 1
while True:
n = 1
while n * a in p:
n += 1
p.add(n * a)
a = n
yield n
def A088178_gen(): # generator of terms
yield 1
p, a = {1}, 1
while True:
n, na = 1, a
while na in p:
n += 1
na += a
p.add(na)
a = n
yield na
def A099378(n):
return (lambda x, y: x // gcd(x, y * n))(divisor_sigma(n), divisor_sigma(n, 0))
def A099377(n):
return (lambda x, y: y * n // gcd(x, y * n))(divisor_sigma(n), divisor_sigma(n, 0))
def A103339(n):
return (lambda x, y: y * n // gcd(x, y * n))(
udivisor_sigma(n), udivisor_sigma(n, 0)
)
def A103340(n):
return (lambda x, y: x // gcd(x, y * n))(udivisor_sigma(n), udivisor_sigma(n, 0))
def A348411_gen():
return filter(
(
lambda n: (lambda x, y: 2 * gcd(x, y * n) == x)(
divisor_sigma(n), divisor_sigma(n, 0)
)
),
count(1),
)
def A066411(n):
b = tuple(comb(n, k) for k in range(n // 2 + 1))
return len(
set(
(
sum(d[i] * b[i] for i in range(n // 2 + 1))
for d in partitionpairs(list(range(n + 1)))
)
)
)
def A348338(n):
m, s = 10**n, set()
for k in range(m):
c, k2, kset = 0, k, set()
while k2 not in kset:
kset.add(k2)
c += 1
k2 = 2 * k2 % m
s.add(c)
return len(s)
def A348339(n):
m, s = 10**n, set()
for k in range(m):
c, k2, kset = 0, k, set()
while k2 not in kset:
kset.add(k2)
c += 1
k2 = k2 * k2 % m
s.add(c)
return len(s)
def A260355_T(n, k): # compute T(n, k)
if k == 1:
return n * (n + 1) // 2
ntuple, count = tuple(range(1, n + 1)), n ** (k + 1)
for s in combinations_with_replacement(permutations(ntuple, n), k - 2):
t = list(ntuple)
for d in s:
for i in range(n):
t[i] *= d[i]
t.sort()
v = 0
for i in range(n):
v += (n - i) * t[i]
if v < count:
count = v
return count
def A219032(n):
s = str(n * n)
m = len(s)
return len(
set(
filter(
lambda x: integer_nthroot(x, 2)[1],
(int(s[i:j]) for i in range(m) for j in range(i + 1, m + 1)),
)
)
)
def A348467(n):
s = str(factorial(n))
m = len(s)
return len(set(int(s[i:j]) for i in range(m) for j in range(i + 1, m + 1)))
def A120004(n):
s = str(n)
m = len(s)
return len(set(int(s[i:j]) for i in range(m) for j in range(i + 1, m + 1)))
def A348428_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = [int(d) for d in str(n)]
m = len(s)
if n == Matrix(m, m, lambda i, j: s[(i + j) % m]).det():
yield n
def A306853_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = [int(d) for d in str(n)]
m = len(s)
if n == Matrix(m, m, lambda i, j: s[(i - j) % m]).per():
yield n
def A219325_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = [int(d) for d in bin(n)[2:]]
m = len(s)
if n == Matrix(m, m, lambda i, j: s[(i - j) % m]).det():
yield n
def A000108_gen(): # generator of terms
yield 1
yield 1
m = 1
for n in count(1):
m = m * (4 * n + 2) // (n + 2)
yield m
@lru_cache(maxsize=None)
def A000700(n):
return (
1
if n == 0
else sum(
(-1) ** (k + 1)
* A000700(n - k)
* prod(
(p ** (e + 1) - 1) // (p - 1) for p, e in factorint(k).items() if p > 2
)
for k in range(1, n + 1)
)
// n
)
def A010815(n):
m = isqrt(24 * n + 1)
return (
0
if m**2 != 24 * n + 1
else ((-1) ** ((m - 1) // 6) if m % 6 == 1 else (-1) ** ((m + 1) // 6))
)
if sys.version_info >= (3, 10):
def A000120(n):
return n.bit_count()
else:
def A000120(n):
return bin(n).count("1")
def A000110_gen():
yield 1
yield 1
blist, b = [1], 1
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
yield b
def A000110(n):
return bell(n)
@lru_cache(maxsize=None)
def A000009(n):
return (
1
if n == 0
else A010815(n)
+ 2 * sum((-1) ** (k + 1) * A000009(n - k**2) for k in range(1, isqrt(n) + 1))
)
def A007953(n):
return sum(int(d) for d in str(n))
def A000984_gen(): # generator of terms
yield 1
m = 1
for n in count(0):
m = m * (4 * n + 2) // (n + 1)
yield m
def A000578(n):
return n**3
def A002808(n):
return composite(n)
def A002808_gen(): # generator of terms
n, m = 3, 5
while True:
for i in range(n + 1, m):
yield i
n, m = m, nextprime(m)
def A000961_gen(): # generator of terms
yield 1
for n in count(2):
if len(factorint(n)) == 1:
yield n
def A002113_gen():
return pal10_gen()
def A003415(n):
return sum((n * e // p for p, e in factorint(n).items())) if n > 1 else 0
def A000265(n):
while not n % 2:
n //= 2
return n
def A001006_gen(): # generator of terms
yield 1
yield 1
m, k = 1, 1
for n in count(2):
m, k = k, (k * (2 * n + 1) + (3 * n - 3) * m) // (n + 2)
yield k
def A000166_gen(): # generator of terms
m, x = 1, 1
for n in count(0):
x, m = x * n + m, -m
yield x
def A004086(n):
return int(str(n)[::-1])
def A001414(n):
return sum(p * e for p, e in factorint(n).items())
def A002144_gen():
for n in count(1):
p = prime(n)
if not (p - 1) % 4:
yield p
def A002182_gen(): # generator of terms
r = 0
for i in count(1):
if (d := divisor_count(i)) > r:
r = d
yield i
def A001700(n):
return comb(2 * n + 1, n + 1)
def A001700_gen(): # generator of terms
b = 1
for n in count(0):
yield b
b = b * (4 * n + 6) // (n + 2)
def A003418(n):
return prod(p ** integerlog(n, p) for p in sieve.primerange(1, n + 1))
def A000111_gen(): # generator of terms
yield from (1, 1)
blist = (0, 1)
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=0)))[-1]
def A014137_gen():
return accumulate(A000108_gen())
def A014138_gen():
return (x - 1 for x in A014137_gen())
def A349866_gen(startvalue=1):
return filter(
lambda m: sum(divisor_sigma(m) % d for d in divisors(m, generator=True)) == m,
count(max(startvalue, 1)),
)
def A005349_gen(startvalue=1):
return filter(
lambda n: not n % sum((int(d) for d in str(n))), count(max(startvalue, 1))
)
def A002322(n):
return reduced_totient(n)
def A006318_gen(): # generator of terms
m, k = 1, 2
yield m
yield k
for n in count(3):
m, k = k, (k * (6 * n - 9) - (n - 3) * m) // n
yield k
def A007913(n):
return prod(p for p, e in factorint(n).items() if e % 2)
def A000178_gen(): # generator of terms
yield 1
n, m = 1, 1
for i in count(1):
m *= i
n *= m
yield n
def A010888(n):
return 1 + (n - 1) % 9
def A000523(n):
return n.bit_length() - 1
def A000583(n):
return n**4
def A000593(n):
return prod((p ** (e + 1) - 1) // (p - 1) for p, e in factorint(n).items() if p > 2)
def A064413_gen(): # generator of terms
yield 1
yield 2
l, s, b = 2, 3, set()
while True:
i = s
while True:
if not i in b and gcd(i, l) > 1:
yield i
l = i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A006218(n):
return 2 * sum(n // k for k in range(1, isqrt(n) + 1)) - isqrt(n) ** 2
def A001694_gen(startvalue=1):
return filter(
lambda n: n == 1 or min(factorint(n).values()) > 1, count(max(startvalue, 1))
)
def A019565(n):
return (
prod(prime(i + 1) for i, v in enumerate(bin(n)[:1:-1]) if v == "1")
if n > 0
else 1
)
def A006882(n):
return factorial2(n)
if sys.version_info >= (3, 10):
def A005187(n):
return 2 * n - n.bit_count()
else:
def A005187(n):
return 2 * n - bin(n).count("1")
def A001003_gen(): # generator of terms
m, k = 1, 1
yield m
yield k
for n in count(3):
m, k = k, (k * (6 * n - 9) - (n - 3) * m) // n
yield k
def A005836(n):
return int(format(n - 1, "b"), 3)
def A002496_gen():
return filter(
isprime, (n + 1 for n in accumulate(count(0), lambda x, y: x + 2 * y - 1))
)
def A052382_gen(startvalue=1):
return filter(lambda n: "0" not in str(n), count(max(startvalue, 1)))
def A003714(n):
tlist, s = [1, 2], 0
while tlist[-1] + tlist[-2] <= n:
tlist.append(tlist[-1] + tlist[-2])
for d in tlist[::-1]:
s *= 2
if d <= n:
s += 1
n -= d
return s
def A026741(n):
return n if n % 2 else n // 2
def A006567_gen():
return filter(
lambda p: str(p) != str(p)[::-1] and isprime(int(str(p)[::-1])),
(prime(n) for n in count(1)),
)
def A006370(n):
q, r = divmod(n, 2)
return 3 * n + 1 if r else q
def A151800(n):
return nextprime(n)
def A051903(n):
return max(factorint(n).values()) if n > 1 else 0
def A001850_gen(): # generator of terms
m, k = 1, 3
yield m
yield k
for n in count(2):
m, k = k, (k * (6 * n - 3) - (n - 1) * m) // n
yield k
def A002293(n):
return comb(4 * n, n) // (3 * n + 1)
def A002293_gen(): # generator of terms
m = 1
yield m
for n in count(0):
m = (
m
* 4
* (4 * n + 3)
* (4 * n + 2)
* (4 * n + 1)
// ((3 * n + 2) * (3 * n + 3) * (3 * n + 4))
)
yield m
def A098550_gen(): # generator of terms
yield from [1, 2, 3]
l1, l2, s, b = 3, 2, 4, set()
while True:
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
yield i
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A001220_gen():
return filter(lambda p: pow(2, p - 1, p * p) == 1, (prime(n) for n in count(1)))
def A047999_T(n, k):
return int(not ~n & k)
@lru_cache(maxsize=None)
def A001175(n):
if n == 1:
return 1
f = factorint(n)
if len(f) > 1:
return lcm(*(A001175(a ** f[a]) for a in f))
else:
k, x = 1, [1, 1]
while x != [0, 1]:
k += 1
x = [x[1], (x[0] + x[1]) % n]
return k
def A066272(n):
return (
len([d for d in divisors(2 * n) if n > d >= 2 and n % d])
+ len([d for d in divisors(2 * n - 1) if n > d >= 2 and n % d])
+ len([d for d in divisors(2 * n + 1) if n > d >= 2 and n % d])
)
@lru_cache(maxsize=None)
def A002321(n):
if n == 0:
return 0
c, j = n, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A002321(k1)
j, k1 = j2, n // j2
return j - c
if sys.version_info >= (3, 10):
def A029837(n):
return n.bit_length() - (1 if n.bit_count() == 1 else 0)
else:
def A029837(n):
return n.bit_length() - (1 if bin(n).count("1") == 1 else 0)
def A007376_gen():
return (int(d) for n in count(0) for d in str(n))
def A054632_gen():
return accumulate(A007376_gen())
def A127353_gen():
return islice(A007376_gen(), 2, None, 2)
def A127050_gen():
return islice(A007376_gen(), 1, None, 2)
def A127950_gen():
return islice(A007376_gen(), 2, None, 8)
def A347345_gen():
return filter(
lambda k: set(str(k * (k + 1) // 2)) <= {"1", "3", "5", "7", "9"},
(int("".join(d)) for l in count(1) for d in product("13579", repeat=l)),
)
def A132739(n):
a, b = divmod(n, 5)
while b == 0:
a, b = divmod(a, 5)
return 5 * a + b
def A349487(n):
a, b = divmod(n * n - 25, 5)
while b == 0:
a, b = divmod(a, 5)
return 5 * a + b
def A349791(n):
b = primepi(n**2) + primepi((n + 1) ** 2) + 1
return (prime(b // 2) + prime((b + 1) // 2)) // 2 if b % 2 else prime(b // 2)
def A000188(n):
return isqrt(n // numbercore(n))
def A020449_gen():
return filter(isprime, (int(format(n, "b")) for n in count(1)))
def A033676(n):
d = divisors(n)
return d[(len(d) - 1) // 2]
def A047994(n):
return prod(p**e - 1 for p, e in factorint(n).items())
def d(n, m):
return not n % m
def A007678(n):
return (
1176 * d(n, 12) * n
- 3744 * d(n, 120) * n
+ 1536 * d(n, 18) * n
- d(n, 2) * (5 * n**3 - 42 * n**2 + 40 * n + 48)
- 2304 * d(n, 210) * n
+ 912 * d(n, 24) * n
- 1728 * d(n, 30) * n
- 36 * d(n, 4) * n
- 2400 * d(n, 42) * n
- 4 * d(n, 6) * n * (53 * n - 310)
- 9120 * d(n, 60) * n
- 3744 * d(n, 84) * n
- 2304 * d(n, 90) * n
+ 2 * n**4
- 12 * n**3
+ 46 * n**2
- 84 * n
) // 48 + 1
def A063990_gen(startvalue=2):
return filter(
lambda n: divisor_sigma(n) - 2 * n
and not divisor_sigma(divisor_sigma(n) - n) - divisor_sigma(n),
count(max(startvalue, 2)),
)
def A051674(n):
return prime(n) ** prime(n)
def A001951(n):
return isqrt(2 * n**2)
def A000587_gen(): # generator of terms
yield 1
yield -1
blist, b = [1], -1
while True:
blist = list(accumulate([b] + blist))
b = -blist[-1]
yield b
def A003132(n):
return sum(int(d) ** 2 for d in str(n))
def A003601_gen(startvalue=1):
return filter(
lambda n: not sum(divisors(n)) % divisor_count(n), count(max(startvalue, 1))
)
@lru_cache(maxsize=None)
def A002088(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * A002088(k1) - 1)
j, k1 = j2, n // j2
return (n * (n - 1) - c + j) // 2
def A045917(n):
return sum(1 for i in range(2, n + 1) if isprime(i) and isprime(2 * n - i))
def A019546_gen():
return filter(
lambda n: set(str(n)) <= {"2", "3", "5", "7"}, (prime(n) for n in count(1))
)
def A011540_gen(startvalue=0):
return filter(lambda n: "0" in str(n), count(max(startvalue, 0)))
def A014963(n):
y = factorint(n)
return list(y.keys())[0] if len(y) == 1 else 1
def A115004(n):
return n**2 + sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i) for i in range(2, n + 1)
)
def A316524(n):
fs = [primepi(p) for p in factorint(n, multiple=True)]
return sum(fs[::2]) - sum(fs[1::2])
def A048050(n):
return 0 if n == 1 else divisor_sigma(n) - n - 1
def A349806(n):
for i in count(n**2 + (n % 2) + 1, 2):
if len(fs := factorint(i)) == 2 == sum(fs.values()):
return i - n**2
def A099610(n):
for i in count(n**2 + (n % 2) + 1, 2):
if len(fs := factorint(i)) == 2 == sum(fs.values()):
return i
def A348762(n):
a, b = divmod(n * n - 64, 2)
while b == 0:
a, b = divmod(a, 2)
return 2 * a + b
def A069834(n):
a, b = divmod(n * n + n, 2)
while b == 0:
a, b = divmod(a, 2)
return 2 * a + b
def A328447(n):
if n == 0:
return 0
s = str(n)
l, s = len(s), "".join(sorted(s.replace("0", "")))
return int(s[0] + "0" * (l - len(s)) + s[1:])
def A005188_gen(): # generator of terms
for k in range(1, 40):
a = tuple(i**k for i in range(10))
yield from (
x[0]
for x in sorted(
filter(
lambda x: x[0] > 0
and tuple(int(d) for d in sorted(str(x[0]))) == x[1],
(
(sum(map(lambda y: a[y], b)), b)
for b in combinations_with_replacement(range(10), k)
),
)
)
)
def A031443_gen(): # generator of terms
for n in count(1):
yield from (
int("1" + "".join(p), 2)
for p in multiset_permutations("0" * n + "1" * (n - 1))
)
def A071925_gen(): # generator of terms
for n in count(1):
yield from (
int("1" + "".join(p))
for p in multiset_permutations("0" * n + "1" * (n - 1))
)
def A349929_gen(): # generator of terms
for n in count(3, 3):
if (
3 * gcd(comb(n * (n * (n + 6) - 6) + 2, 6 * n * (n - 1) + 3), n**3)
== n**3
):
yield n
def A349509(n):
return n**3 // gcd(comb(n * (n * (n + 6) - 6) + 2, 6 * n * (n - 1) + 3), n**3)
def A099611(n):
for i in count(n**2 - (n % 2) - 1, -2):
fs = factorint(i)
if len(fs) == 2 == sum(fs.values()):
return i
def A349809(n):
for i in count(n**2 - (n % 2) - 1, -2):
fs = factorint(i)
if len(fs) == 2 == sum(fs.values()):
return n**2 - i
def A002982_gen(startvalue=1):
return filter(lambda n: isprime(factorial(n) - 1), count(max(startvalue, 1)))
def A000058_gen(): # generator of terms
yield (a := 2)
while True:
a = a * (a - 1) + 1
yield a
def A151799(n):
return prevprime(n)
def A000078_gen(): # generator of terms
b = [0, 0, 0, 1]
yield from b
while True:
yield (c := sum(b))
b = b[1:] + [c]
def A002054(n):
return comb(2 * n + 1, n - 1)
def A006720_gen(): # generator of terms
b = [1, 1, 1, 1]
yield from b
while True:
yield (c := (b[-1] * b[-3] + b[-2] ** 2) // b[-4])
b = b[1:] + [c]
def A033677(n):
return (lambda d: d[len(d) // 2])(divisors(n))
def A078972_gen(): # generator of terms
for n in count(0):
yield from sorted(
prod(p)
for p in combinations_with_replacement(
sieve.primerange(10**n, 10 ** (n + 1)), 2
)
)
def A005493_gen(): # generator of terms
blist, b = [1], 1
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
yield blist[-2]
def A188014(n):
return (
int((isqrt(5 * n**2) + n) // 2 - (isqrt(5 * (n - 4) ** 2) + n) // 2 - 4)
if n > 3
else 1 - (n % 2)
)
def A348209(n):
if n > 2 and bin(n).count("1") == 1:
return 0
k, m, n1, n2, n3 = 1, 2, n ** (n - 2), n ** (n - 1), n**n
while m < n2:
k += 1
m = (2 * m) % n3
while k <= n3:
if m >= n1:
a = ispandigital0(m, n)
if a[0] and ((not a[1]) or m >= n2):
return k
k += 1
m = (2 * m) % n3
return 0
def A000978_gen():
return filter(lambda p: isprime((2**p + 1) // 3), (prime(n) for n in count(2)))
def A007500_gen():
return filter(lambda p: isprime(int(str(p)[::-1])), (prime(n) for n in count(1)))
def A010784_gen(startvalue=0):
return filter(lambda n: len(set(str(n))) == len(str(n)), count(max(startvalue, 0)))
def A050278_gen():
return (
int(e + "".join(d))
for e in "123456789"
for d in permutations("0123456789".replace(e, ""), 9)
)
def A071924(n):
return primepi(
max(
primefactors(
next(
islice(
(
int(e + "".join(d))
for e in "123456789"
for d in permutations("0123456789".replace(e, ""), 9)
),
n - 1,
None,
)
)
)
)
)
def A071924_gen():
return (
primepi(max(primefactors(m)))
for m in (
int(e + "".join(d))
for e in "123456789"
for d in permutations("0123456789".replace(e, ""), 9)
)
)
def A000538(n):
return n * (n**2 * (n * (6 * n + 15) + 10) - 1) // 30
def A330151(n):
return 8 * n * (n**2 * (n * (6 * n + 15) + 10) - 1) // 15
def A259317(n):
return n * (n * (n**2 * (n * (16 * n + 48) + 40) - 11) - 3) // 45
def A254640(n):
return (
n
* (
n
* (
n
* (
n * (n * (n * (n * (n * (10 * n + 135) + 720) + 1890) + 2394) + 945)
- 640
)
- 450
)
+ 36
)
// 5040
)
def A002109_gen():
return accumulate((k**k for k in count(0)), mul)
def A002109(n):
return prod(k**k for k in range(1, n + 1))
@lru_cache(maxsize=None)
def A018805(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A018805(k1)
j, k1 = j2, n // j2
return n * (n - 1) - c + j
def A023194_gen(): # generator of terms
yield 2
yield from filter(lambda n: isprime(divisor_sigma(n)), (n**2 for n in count(1)))
def A010057(n):
return int(integer_nthroot(n, 3)[1])
def A001286(n):
return (n - 1) * factorial(n) // 2
def A001286_gen(): # generator of terms
b = 1
yield b
for n in count(2):
b = b * n * (n + 1) // (n - 1)
yield b
def A007602_gen(startvalue=1):
return filter(
lambda n: not ("0" in str(n) or n % prod(int(d) for d in str(n))),
count(max(startvalue, 1)),
)
def A001608_gen(): # generator of terms
a, b, c = 3, 0, 2
yield from (a, b, c)
while True:
a, b, c = b, c, a + b
yield c
def A031971(n):
return harmonic(n, -n)
def A348470(n):
return 1 if n == 1 else min(primefactors(next(islice(A064413_gen(), n - 1, None))))
def A348470_gen():
yield from (min(primefactors(n)) if n > 1 else 1 for n in A064413_gen())
def A349662(n):
return 0 if n <= 1 else isqrt(n**3 - 1) - n
def A349993(n):
return isqrt(n**3) - n + 1
def A349792_gen(): # generator of terms
p1 = 0
for n in count(1):
p2 = primepi((n + 1) ** 2)
b = p1 + p2 + 1
if b % 2:
p = prime(b // 2)
q = nextprime(p)
if p + q == 2 * n * (n + 1):
yield n
p1 = p2
def A308533_gen(startvalue=3): # generator of terms
for n in count(max(startvalue, 3)):
a = antidivisors(n)
if int("".join(str(s) for s in a)) % sum(a) == 0:
yield n
def A130846(n):
return int("".join(str(s) for s in antidivisors(n)))
def A003278(n):
return int(format(n - 1, "b"), 3) + 1
def A000539(n):
return n**2 * (n**2 * (n * (2 * n + 6) + 5) - 1) // 12
def A027868_gen():
yield from [0] * 5
p5 = 0
for n in count(5, 5):
p5 += multiplicity(5, n)
yield from [p5] * 5
def A187950(n):
return int((isqrt(5 * (n + 4) ** 2) + n) // 2 - (isqrt(5 * n**2) + n) // 2 - 4)
def A018900_gen():
return (2**a + 2**b for a in count(1) for b in range(a))
@lru_cache(maxsize=None)
def A005728(n): # based on second formula in A018805
if n == 0:
return 1
c, j = -2, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * A005728(k1) - 3)
j, k1 = j2, n // j2
return (n * (n - 1) - c + j) // 2
def A007629_gen(startvalue=10): # generator of terms
for n in count(max(startvalue, 10)):
x = [int(d) for d in str(n)]
y = sum(x)
while y < n:
x, y = x[1:] + [y], 2 * y - x[0]
if y == n:
yield n
def A007774_gen(startvalue=1):
return filter(lambda n: len(primefactors(n)) == 2, count(max(startvalue, 1)))
def A009994_gen(): # generator of terms
yield 0
yield from (
int("".join(i))
for l in count(1)
for i in combinations_with_replacement("123456789", l)
)
def A004159(n):
return sum(int(d) for d in str(n * n))
def A001952(n):
return 2 * n + isqrt(2 * n**2)
def A005917(n):
return n * (n * (4 * n - 6) + 4) - 1
def A031347(n):
while n > 9:
n = prod(int(d) for d in str(n))
return n
def A069010(n):
return sum(1 for d in bin(n)[2:].split("0") if len(d))
def A005823(n):
return 2 * int(format(n - 1, "b"), 3)
def A014311_gen():
return (
2**a + 2**b + 2**c
for a in count(2)
for b in range(1, a)
for c in range(b)
)
def A349783(n):
return sum(abs(stirling(2 * n, j, kind=1)) for j in range(n + 1))
def A011971_gen(): # generator of terms
blist = [1]
yield 1
while True:
b = blist[-1]
blist = list(accumulate([b] + blist))
yield from blist
def A046936_gen(): # generator of terms
yield 0
blist = [1, 1]
yield from blist
while True:
b = blist[-1]
blist = list(accumulate([b] + blist))
yield from blist
def A349960(n):
if n <= 2:
return 3 - n
a, b = "", ""
for i in count(1, 2):
a += str(i)
b += str(i + 1)
ai, bi = int(a), int(b)
if len(a) + n - 2 == len(b):
return bi // ai
m = 10 ** (n - 2 - len(b) + len(a))
lb = bi * m // (ai + 1)
ub = (bi + 1) * m // ai
if lb == ub:
return lb
def A349958(n):
for j in range(n + 1):
for k in range(j + 1):
if comb(j, k) % n == 0:
return j
def A045918(n):
return int(
"".join(
[str(len(m.group(0))) + m.group(0)[0] for m in finditer(r"(\d)\1*", str(n))]
)
)
def A001602(n):
a, b, i, p = 0, 1, 1, prime(n)
while b % p:
a, b, i = b, (a + b) % p, i + 1
return i
def A014577(n):
s = bin(n + 1)[2:]
m = len(s)
i = s[::-1].find("1")
return 1 - int(s[m - i - 2]) if m - i - 2 >= 0 else 1
def A081145_gen(): # generator of terms
yield from [1, 2]
l, s, b1, b2 = 2, 3, set(), set([1])
for n in count(3):
i = s
while True:
m = abs(i - l)
if not (i in b1 or m in b2):
yield i
b1.add(i)
b2.add(m)
l = i
while s in b1:
b1.remove(s)
s += 1
break
i += 1
def A000127(n):
return n * (n * (n * (n - 6) + 23) - 18) // 24 + 1
def A007407(n):
return sum(Fraction(1, k**2) for k in range(1, n + 1)).denominator
def A039724(n):
s, q = "", n
while q >= 2 or q < 0:
q, r = divmod(q, -2)
if r < 0:
q += 1
r += 2
s += str(r)
return int(str(q) + s[::-1])
def A065855(n):
return 0 if n < 4 else n - primepi(n) - 1
def A004290(n):
if n > 0:
for i in range(1, 2**n):
x = int(bin(i)[2:])
if not x % n:
return x
return 0
def A006521_gen(startvalue=1):
return filter(lambda n: pow(2, n, n) == n - 1, count(max(startvalue, 1)))
def A124240_gen(startvalue=1):
return filter(lambda n: n % reduced_totient(n) == 0, count(max(startvalue, 1)))
def A289257_gen(startvalue=1):
return filter(
lambda n: 2 * n % reduced_totient(2 * n) == 0 and pow(2, n, n) == n - 1,
count(max(startvalue, 1)),
)
def A306302(n):
return 2 * n * (n + 1) + sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i) for i in range(2, n + 1)
)
def A307720_gen(): # generator of terms. Greedy algorithm
yield 1
c, b = Counter(), 1
while True:
k, kb = 1, b
while c[kb] >= kb:
k += 1
kb += b
c[kb] += 1
b = k
yield k
def A007569(n):
return (
2
if n == 2
else n
* (
42 * (not n % 12)
- 144 * (not n % 120)
+ 60 * (not n % 18)
- 96 * (not n % 210)
+ 35 * (not n % 24)
- 38 * (not n % 30)
- 82 * (not n % 42)
- 330 * (not n % 60)
- 144 * (not n % 84)
- 96 * (not n % 90)
)
+ (
n**4
- 6 * n**3
+ 11 * n**2
+ 18 * n
- (not n % 2) * (5 * n**3 - 45 * n**2 + 70 * n - 24)
- 36 * (not n % 4) * n
- 4 * (not n % 6) * n * (45 * n - 262)
)
// 24
)
def A003401_gen(startvalue=1):
return filter(
lambda n: format(totient(n), "b").count("1") == 1, count(max(startvalue, 1))
)
def A014127_gen():
return filter(lambda p: pow(3, p - 1, p * p) == 1, (prime(n) for n in count(1)))
def A031346(n):
mp = 0
while n > 9:
n = prod(int(d) for d in str(n))
mp += 1
return mp
def A029967_gen():
return filter(lambda n: is_pal(n, 12), pal10_gen())
def A029968_gen():
return filter(lambda n: is_pal(n, 13), pal10_gen())
def A049445_gen(startvalue=1):
return filter(
lambda n: not n % sum([int(d) for d in bin(n)[2:]]), count(max(startvalue, 1))
)
def A348623_gen(): # generator of terms
n = 1
yield n
while True:
n = prod(q + 1 for p, q in factorint(n).items() if p > 2)
yield n
def A349775_helper(n): # generate sums of 2 subsets A,B with |A|,|B| >= 2 for A349775
for l in range(2, n + 2):
for a in combinations(range(n + 1), l):
amax = max(a)
bmax = min(amax, n - amax)
for lb in range(2, bmax + 2):
for b in combinations(range(bmax + 1), lb):
yield tuple(sorted(set(x + y for x in a for y in b)))
def A349775(n):
c = Counter()
for s in set(A349775_helper(n)):
c[len(s)] += 1
for i in range(n + 1, 1, -1):
if c[i] < comb(n + 1, i):
return i
def A002779_gen():
return filter(lambda n: str(n) == str(n)[::-1], (n**2 for n in count(0)))
def A004185(n):
return int("".join(sorted(str(n))).replace("0", "")) if n > 0 else 0
def A029731_gen():
return filter(lambda n: is_pal(n, 16), pal10_gen())
def A029804_gen():
return filter(lambda n: is_pal(n, 8), pal10_gen())
def A037861(n):
return 2 * format(n, "b").count("0") - len(format(n, "b"))
def A056608(n):
return min(factorint(composite(n)))
def A006261(n):
return (n * (n * (n * (n * (n - 5) + 25) + 5) + 94) + 120) // 120
def A006561(n):
return (
0
if n == 2
else n
* (
42 * (not n % 12)
- 144 * (not n % 120)
+ 60 * (not n % 18)
- 96 * (not n % 210)
+ 35 * (not n % 24)
- 38 * (not n % 30)
- 82 * (not n % 42)
- 330 * (not n % 60)
- 144 * (not n % 84)
- 96 * (not n % 90)
)
+ (
n**4
- 6 * n**3
+ 11 * n**2
- 6 * n
- (not n % 2) * (5 * n**3 - 45 * n**2 + 70 * n - 24)
- 36 * (not n % 4) * n
- 4 * (not n % 6) * n * (45 * n - 262)
)
// 24
)
def A001129_gen(): # generator of terms
r1, r2 = 1, 0
yield r2
yield r1
while True:
l, r2 = r1 + r2, r1
r1 = int(str(l)[::-1])
yield l
def A034838_gen(): # generator of terms
for g in count(1):
for n in product("123456789", repeat=g):
s = "".join(n)
m = int(s)
if not any(m % int(d) for d in s):
yield m
def A076479(n):
return mobius(prod(primefactors(n)))
def A229037_gen(): # generator of terms
blist = []
for n in count(0):
i, j, b = 1, 1, set()
while n - 2 * i >= 0:
b.add(2 * blist[n - i] - blist[n - 2 * i])
i += 1
while j in b:
b.remove(j)
j += 1
blist.append(j)
yield j
def A034709_gen(startvalue=1):
return filter(lambda n: n % 10 and not n % (n % 10), count(max(startvalue, 1)))
def A051802(n):
if n == 0:
return 1
while n > 9:
n = prod(int(d) for d in str(n) if d != "0")
return n
def A054977(n):
return 1 if n else 2
def A084937_gen(): # generator of terms
yield from [1, 2]
l1, l2, s, b = 2, 1, 3, set()
while True:
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) == 1:
yield i
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A099165_gen():
return filter(lambda n: is_pal(n, 32), pal10_gen())
def A133500(n):
s = str(n)
l = len(s)
m = int(s[-1]) if l % 2 else 1
for i in range(0, l - 1, 2):
m *= int(s[i]) ** int(s[i + 1])
return m
def A023109(n):
if n > 0:
k = 0
while True:
m = k
for i in range(n):
if str(m) == str(m)[::-1]:
break
m += int(str(m)[::-1])
else:
if str(m) == str(m)[::-1]:
return k
k += 1
else:
return 0
def A023330_gen():
return filter(
lambda p: all((isprime(2**m * (p + 1) - 1) for m in range(1, 6))),
(prime(n) for n in count(1)),
)
def A071321(n):
fs = factorint(n, multiple=True)
return sum(fs[::2]) - sum(fs[1::2])
def A290447(n):
p, p2 = set(), set()
for b, c, d in combinations(range(1, n), 3):
e = b + d - c
f1, f2, g = (
Fraction(b * d, e),
Fraction(b * d * (c - b) * (d - c), e**2),
(n - 1) * e - 2 * b * d,
)
for i in range(n - d):
if 2 * i * e < g:
p2.add((i + f1, f2))
elif 2 * i * e == g:
p.add(f2)
else:
break
return len(p) + 2 * len(p2)
def A000387_gen(): # generator of terms
m, x = 1, 0
for n in count(0):
x, m = x * n + m * (n * (n - 1) // 2), -m
yield x
def A003893_gen(): # generator of terms
a, b, = (
0,
1,
)
yield a
while True:
a, b = b, (a + b) % 10
yield a
def A051801(n):
return prod(int(d) for d in str(n) if d != "0") if n > 0 else 1
def A001917(n):
p = prime(n)
return 1 if n == 2 else (p - 1) // n_order(2, p)
def A007540_gen(): # generator of terms
for n in count(1):
p, m = prime(n), 1
p2 = p * p
for i in range(2, p):
m = (m * i) % p2
if m == p2 - 1:
yield p
def A027870(n):
return str(2**n).count("0")
def A029955_gen():
return pal_gen(9)
def A061910_gen(startvalue=1):
return filter(
lambda n: is_square(sum(int(d) for d in str(n * n))), count(max(startvalue, 1))
)
def A006721_gen(): # generator of terms
blist = [1, 1, 1, 1, 1]
yield from blist
for n in count(5):
blist = blist[1:] + [
(blist[-1] * blist[-4] + blist[-2] * blist[-3]) // blist[-5]
]
yield blist[-1]
def A087062_T(n, k):
return lunar_mul(n, k)
def A007488_gen():
return filter(lambda p: is_square(int(str(p)[::-1])), (prime(n) for n in count(1)))
def A059758_gen(): # generator of terms
for l in count(1):
for a in "1379":
for b in "0123456789":
if a != b and isprime(p := int((a + b) * l + a)):
yield p
def A175046(n):
return int(
"".join(
d + "1" if "1" in d else d + "0"
for d in split("(0+)|(1+)", bin(n)[2:])
if d != "" and d != None
),
2,
)
def A228407_gen(): # generator of terms
yield from [0, 11]
l, s, b = Counter("11"), 1, {11}
while True:
i = s
while True:
if i not in b:
li, o = Counter(str(i)), 0
for d in (l + li).values():
if d % 2:
if o > 0:
break
o += 1
else:
yield i
l = li
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A317081(n):
if n == 0:
return 1
c = 0
for d in partitions(n):
s = set(d.values())
if len(s) == max(s):
c += 1
return c
def A000979_gen():
return filter(isprime, ((2 ** prime(n) + 1) // 3 for n in count(2)))
def A004094(n):
return int(str(2**n)[::-1])
def A029954_gen():
return pal_gen(7)
def A036691(n):
return factorial(composite(n)) // primorial(primepi(composite(n))) if n > 0 else 1
def A054377_gen(startvalue=2):
return filter(
lambda n: sum(n / p for p in primefactors(n)) + 1 == n,
count(max(startvalue, 2)),
)
def A227349(n):
return prod(len(d) for d in split("0+", bin(n)[2:]) if d) if n > 0 else 1
def A000540(n):
return n * (n**2 * (n**2 * (n * (6 * n + 21) + 21) - 7) + 1) // 42
def A034947(n):
s = bin(n)[2:]
m = len(s)
i = s[::-1].find("1")
return 1 - 2 * int(s[m - i - 2]) if m - i - 2 >= 0 else 1
def A049060(n):
return prod((p ** (e + 1) - 2 * p + 1) // (p - 1) for p, e in factorint(n).items())
def A057890_gen(startvalue=0):
return filter(
lambda n: bin(n)[2:].rstrip("0") == bin(n)[2:].rstrip("0")[::-1],
count(max(startvalue, 0)),
)
@lru_cache(maxsize=None)
def A015614(n): # based on second formula in A018805
if n == 0:
return -1
c, j = 2, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * A015614(k1) + 1)
j, k1 = j2, n // j2
return (n * (n - 1) - c + j) // 2
def A045875(n):
l, x = [str(d) * n for d in range(10)], 1
for m in count(0):
s = str(x)
for k in l:
if k in s:
return m
x *= 2
def A080670(n):
return (
1
if n == 1
else int(
"".join([str(y) for x in sorted(factorint(n).items()) for y in x if y != 1])
)
)
def A006590(n):
return (lambda m: n + 2 * sum((n - 1) // k for k in range(1, m + 1)) - m * m)(
isqrt(n - 1)
)
def A006794_gen(): # generator of terms
p, q = 2, 2
while True:
if isprime(q - 1):
yield p
p = nextprime(p)
q *= p
def A036229(n):
k, r, m = (10**n - 1) // 9, 2**n - 1, 0
while m <= r:
t = k + int(bin(m)[2:])
if isprime(t):
return t
m += 1
return -1
def A047842(n):
s, x = "", str(n)
for i in range(10):
y = str(i)
c = str(x.count(y))
if c != "0":
s += c + y
return int(s)
def A233466_gen(startvalue=1):
return filter(
lambda n: 2 * totient(n) == n - 5,
count(max(startvalue + 1 - startvalue % 2, 1), 2),
)
def A078971_gen(): # generator of terms
for t in count(0):
yield (2 ** (2 * t) - 1) // 3
yield from ((2 ** (2 * t + 1) + 2 ** (2 * j + 1) - 1) // 3 for j in range(t))
def A048054(n):
return len(
[p for p in primerange(10 ** (n - 1), 10**n) if isprime(int(str(p)[::-1]))]
)
def A059729(n):
s = [int(d) for d in str(n)]
l = len(s)
t = [0] * (2 * l - 1)
for i in range(l):
for j in range(l):
t[i + j] = (t[i + j] + s[i] * s[j]) % 10
return int("".join(str(d) for d in t))
if sys.version_info >= (3, 10):
def A159918(n):
return n * n.bit_count()
else:
def A159918(n):
return bin(n * n).count("1")
def A061712(n):
l, k = n - 1, 2**n
while True:
for d in combinations(range(l - 1, -1, -1), l - n + 1):
m = k - 1 - sum(2 ** (e) for e in d)
if isprime(m):
return m
l += 1
k *= 2
def A110566(n):
return lcm([k for k in range(1, n + 1)]) // harmonic(n).q
def A256630_gen(): # generator of terms
for l in count(0):
for a in ("1", "2", "3", "4"):
for b in product("01234", repeat=l):
for c in ("0", "1", "2"):
s = a + "".join(b) + c
if "0" in s and "4" in s:
n = int(s)
s2 = set(str(n**2))
if {"0", "4"} <= s2 <= {"0", "1", "2", "3", "4"}:
yield n
def A007608(n):
s, q = "", n
while q >= 4 or q < 0:
q, r = divmod(q, -4)
if r < 0:
q += 1
r += 4
s += str(r)
return int(str(q) + s[::-1])
def A000139_gen(): # generator of terms
b = 2
yield b
for n in count(1):
b = 3 * (3 * n - 2) * (3 * n - 1) * b // (2 * n + 2) // (2 * n + 1)
yield b
def A000139(n):
return 2 if n == 0 else 2 * comb(3 * n, n - 1) // n // (n + 1)
def A065197_gen(startvalue=1):
return filter(
lambda n: n
== reduce(lambda m, k: m + (k if (m // k) % 2 else -k), range(n, 1, -1), n),
count(max(startvalue, 1)),
)
def A014847_gen(): # generator of terms
b = 1
for n in count(1):
if not b % n:
yield n
b = b * (4 * n + 2) // (n + 2)
def A050486(n):
return (2 * n + 7) * comb(n + 6, 6) // 7
def A053347(n):
return (n + 4) * comb(n + 7, 7) // 4
def A057147(n):
return n * sum(int(d) for d in str(n))
def A063655(n):
d = divisors(n)
l = len(d)
return d[(l - 1) // 2] + d[l // 2]
def A074832_gen():
return filter(
lambda p: isprime(int(bin(p)[:1:-1], 2)), (prime(n) for n in count(1))
)
def A175498_gen(): # generator of terms
yield from [1, 2]
l, s, b1, b2 = 2, 3, set(), {1}
for n in count(3):
i = s
while True:
if not (i in b1 or i - l in b2):
yield i
b1.add(i)
b2.add(i - l)
l = i
while s in b1:
b1.remove(s)
s += 1
break
i += 1
def A000475_gen(): # generator of terms
m, x = 1, 0
for n in count(4):
x, m = x * n + m * comb(n, 4), -m
yield x
def A003684(n):
return len(
[
p
for p in primerange(10 ** (n - 1), 10**n)
if len(set(str(p))) == len(str(p)) and isprime(int(str(p)[::-1]))
]
)
def A007497_gen():
return accumulate(repeat(2), lambda x, _: divisor_sigma(x))
def A031877_gen(): # generator of terms
for n in count(1):
if n % 10:
s1 = str(n)
s2 = s1[::-1]
if s1 != s2 and not n % int(s2):
yield n
def A038189(n):
s = bin(n)[2:]
m = len(s)
i = s[::-1].find("1")
return int(s[m - i - 2]) if m - i - 2 >= 0 else 0
@lru_cache(maxsize=None)
def A071778(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A071778(k1)
j, k1 = j2, n // j2
return n * (n**2 - 1) - c + j
def A078241(n):
if n > 0:
for i in range(1, 2**n):
x = 2 * int(bin(i)[2:])
if not x % n:
return x
return 0
def A161710(n):
return (
n
* (
n * (n * (n * (n * (n * (154 - 6 * n) - 1533) + 7525) - 18879) + 22561)
- 7302
)
// 2520
+ 1
)
def A161713(n):
return n * (n * (n * (n * (15 - n) - 65) + 125) - 34) // 40 + 1
def A250408_gen():
return filter(lambda n: is_pal(n, 20), pal10_gen())
def A345957(n):
if n == 1:
return 1
fs = factorint(n, multiple=True)
q, r = divmod(len(fs), 2)
return 0 if r else len(list(multiset_combinations(fs, q)))
def A004520(n):
return int("".join(str(2 * int(d) % 10) for d in str(n)))
def A005807_gen(): # generator of terms
b = 2
yield b
for n in count(0):
b = b * (4 * n + 2) * (5 * n + 9) // ((n + 3) * (5 * n + 4))
yield b
def A014707(n):
s = bin(n + 1)[2:]
m = len(s)
i = s[::-1].find("1")
return int(s[m - i - 2]) if m - i - 2 >= 0 else 0
def A031423_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
cf = continued_fraction_periodic(0, 1, n)
if (
len(cf) > 1
and len(cf[1]) > 1
and len(cf[1]) % 2
and cf[1][len(cf[1]) // 2] == 10
):
yield n
def A114043(n):
return (
4 * n**2
- 6 * n
+ 3
+ 2 * sum(totient(i) * (n - i) * (2 * n - i) for i in range(2, n))
)
def A249156_gen():
return filter(lambda n: is_pal(n, 7), pal_gen(5))
def A250410_gen():
return filter(lambda n: is_pal(n, 25), pal10_gen())
def A000449_gen(): # generator of terms
m, x = 1, 0
for n in count(3):
x, m = x * n + m * (n * (n - 1) * (n - 2) // 6), -m
yield x
def A000541(n):
return n**2 * (n**2 * (n**2 * (n * (3 * n + 12) + 14) - 7) + 2) // 24
def A001287(n):
return comb(n, 10)
def A022842(n):
return isqrt(8 * n**2)
def A031286(n):
ap = 0
while n > 9:
n = sum(int(d) for d in str(n))
ap += 1
return ap
def A055165(n):
return sum(1 for s in product([0, 1], repeat=n**2) if Matrix(n, n, s).det() != 0)
def A145768(n):
return reduce(xor, (x**2 for x in range(n + 1)))
def A145829_gen(): # generator of terms
m = 0
for n in count(1):
m ^= n**2
a, b = integer_nthroot(m, 2)
if b:
yield a
def A249155_gen():
return filter(lambda n: is_pal(n, 15), pal_gen(6))
def A145828_gen(): # generator of terms
m = 0
for n in count(0):
m ^= n**2
if isqrt(m) ** 2 == m:
yield m
def A193232(n):
return reduce(xor, (x * (x + 1) for x in range(n + 1))) // 2
def A062700_gen(): # generator of terms
yield 3
yield from filter(isprime, (divisor_sigma(d**2) for d in count(1)))
def A065710(n):
return str(2**n).count("2")
def A215732(n):
l, x = [str(d) * n for d in range(10)], 1
while True:
s = str(x)
for k in range(10):
if l[k] in s:
return k
x *= 2
def A260343_gen(startvalue=2):
return filter(
lambda n: isprime(
intbase(list(range(1, n)) + [1, 0] + list(range(n - 1, 0, -1)), n)
),
count(max(startvalue, 2)),
)
def A320486(n):
return int("0" + "".join(d if str(n).count(d) == 1 else "" for d in str(n)))
def A002708_gen(): # generator of terms
a, b = 1, 1
for n in count(1):
yield a % n
a, b = b, a + b
def A003098_gen():
return filter(
lambda m: str(m) == str(m)[::-1], (n * (n + 1) // 2 for n in count(0))
)
def A005001_gen(): # generator of terms
yield from [0, 1, 2]
blist, a, b = [1], 2, 1
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
a += b
yield a
def A006533(n):
return (
1176 * (not n % 12) * n
- 3744 * (not n % 120) * n
+ 1536 * (not n % 18) * n
- (not n % 2) * (5 * n**3 - 42 * n**2 + 40 * n + 48)
- 2304 * (not n % 210) * n
+ 912 * (not n % 24) * n
- 1728 * (not n % 30) * n
- 36 * (not n % 4) * n
- 2400 * (not n % 42) * n
- 4 * (not n % 6) * n * (53 * n - 310)
- 9120 * (not n % 60) * n
- 3744 * (not n % 84) * n
- 2304 * (not n % 90) * n
+ 2 * n**4
- 12 * n**3
+ 46 * n**2
- 36 * n
) // 48 + 1
def A018796(n):
if n == 0:
return 0
else:
d, nd = 1, n
while True:
x = (isqrt(nd - 1) + 1) ** 2
if x < nd + d:
return int(x)
d *= 10
nd *= 10
def A027611(n):
return (n * harmonic(n)).q
def A037015_gen(startvalue=0): # generator of terms
for n in count(max(startvalue, 0)):
c = None
for x, y in groupby(bin(n)[2:]):
z = len(list(y))
if c != None and z >= c:
break
c = z
else:
yield n
def A038003_gen(): # generator of terms
yield from [1, 1]
c, s = 1, 3
for n in count(2):
c = (c * (4 * n - 2)) // (n + 1)
if n == s:
yield c
s = 2 * s + 1
def A050782(n):
if n % 10:
for i in islice(pal10_gen(), 1, None):
q, r = divmod(i, n)
if not r:
return q
else:
return 0
def A073327(n):
return sum(ord(d) - 96 for d in sub(r"\sand\s|[^a-z]", "", num2words(n)))
def A088177(): # generator of terms
yield 1
yield 1
p, a = {1}, 1
while True:
n = 1
while n * a in p:
n += 1
p.add(n * a)
a = n
yield n
def A096497(n):
return nextprime((10**n - 1) // 9)
def A101337(n):
s = str(n)
l = len(s)
return sum(int(d) ** l for d in s)
def A141255(n):
return 2 * (n - 1) * (2 * n - 1) + 2 * sum(
totient(i) * (n - i) * (2 * n - i) for i in range(2, n)
)
def A176774(n):
k = (isqrt(8 * n + 1) - 1) // 2
while k >= 2:
a, b = divmod(2 * (k * (k - 2) + n), k * (k - 1))
if not b:
return a
k -= 1
def A002131(n):
return prod(
p**e if p == 2 else (p ** (e + 1) - 1) // (p - 1)
for p, e in factorint(n).items()
)
def A024916(n):
return sum(k * (n // k) for k in range(1, n + 1))
def A350146(n):
return sum(k * (n // k) for k in range(1, n + 1)) - sum(
k * (n // 2 // k) for k in range(1, n // 2 + 1)
)
def A252867_gen(): # generator of terms
yield from [0, 1, 2]
l1, l2, s, b = 2, 1, 3, set()
while True:
i = s
while True:
if not (i in b or i & l1) and i & l2:
yield i
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A002419(n):
return (6 * n - 2) * comb(n + 2, 3) // 4
def A015950_gen(startvalue=1):
return filter(lambda n: pow(4, n, n) == n - 1, count(max(startvalue, 1)))
def A016069_gen(): # generator of terms
for g in count(2):
n, blist = 2**g - 1, []
for x in combinations("0123456789", 2):
for i, y in enumerate(product(x, repeat=g)):
if i > 0 and i < n and y[0] != "0":
z = int("".join(y))
a, b = integer_nthroot(z, 2)
if b:
blist.append(a)
yield from sorted(blist)
def A350092(n):
return floor((1 + sqrt(5) / 2) ** n)
def A014217(n):
return floor(((1 + sqrt(5)) / 2) ** n)
def A350174_gen():
return chain.from_iterable([k] * prime(k + 1) for k in count(0))
def A350173(n):
return prime(n) ** (n % 2 + 1)
def A350171(n):
return prime(n) + n % 2
def A349425(n):
if n % 10 == 0:
return 0
m, n1, n2 = n, 10**n, 10 ** (n - 1)
while (k := pow(n, m, n1)) != m:
m = k
return k // n2
def A309081(n):
return n + sum((1 if k % 2 else -1) * (n // k**2) for k in range(2, isqrt(n) + 1))
def A055882_gen(): # generator of terms
yield from [1, 2]
blist, b, n2 = [1], 1, 4
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
yield b * n2
n2 *= 2
def A068679_gen(): # generator of terms
for n in count(1):
if isprime(10 * n + 1):
s = str(n)
for i in range(len(s)):
if not isprime(int(s[:i] + "1" + s[i:])):
break
else:
yield n
def A082183(n):
t = n * (n + 1)
ds = divisors(t)
for i in range(len(ds) // 2 - 2, -1, -1):
x = ds[i]
y = t // x
a, b = divmod(y - x, 2)
if b:
return a
return -1
def A098464_gen(): # generator of terms
l, h = 1, Fraction(1, 1)
for k in count(1):
l = lcm(l, k)
h += Fraction(1, k)
if l == h.denominator:
yield k
def A109812_gen(): # generator of terms
yield 1
l1, s, b = 1, 2, set()
while True:
i = s
while True:
if not (i in b or i & l1):
yield i
l1 = i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A132106(n):
return (lambda m: 2 * (sum(n // k for k in range(1, m + 1))) + m * (1 - m) + 1)(
isqrt(n)
)
def A215727(n):
l, x = [str(d) * n for d in range(10)], 1
for m in count(0):
s = str(x)
for k in l:
if k in s:
return m
x *= 3
def A000542(n):
return (
n
* (n**2 * (n**2 * (n**2 * (n * (10 * n + 45) + 60) - 42) + 20) - 3)
// 90
)
def A002796_gen(startvalue=1):
return filter(
lambda n: all((d == "0" or n % int(d) == 0) for d in set(str(n))),
count(max(startvalue, 1)),
)
def A004167(n):
return int(str(3**n)[::-1])
def A014312_gen():
return (
2**a + 2**b + 2**c + 2**d
for a in count(3)
for b in range(2, a)
for c in range(1, b)
for d in range(c)
)
def A046732_gen():
return filter(
lambda p: len(str(p)) == len(set(str(p))) and isprime(int(str(p)[::-1])),
(prime(n) for n in count(1)),
)
def A050985(n):
return 1 if n <= 1 else prod(p ** (e % 3) for p, e in factorint(n).items())
def A061242_gen():
return filter(lambda p: not (p + 1) % 18, (prime(n) for n in count(1)))
def A061762(n):
return sum(a := [int(d) for d in str(n)]) + prod(a)
def A219324_gen(): # generator of terms
for n in count(1):
s = [int(d) for d in str(n)]
m = len(s)
if n == Matrix(m, m, lambda i, j: s[(i - j) % m]).det():
yield n
def A246544_gen(): # generator of terms
for m in count(1):
n = composite(m)
x = divisors(n)
x.pop()
y = sum(x)
while y < n:
x, y = x[1:] + [y], 2 * y - x[0]
if y == n:
yield n
def A276037_gen():
yield from (int("".join(d)) for l in count(1) for d in product("15", repeat=l))
def A290131(n):
return 2 * (n - 1) ** 2 + sum(
totient(i) * (n - i) * (2 * n - i) for i in range(2, n)
)
def A317087_gen(): # generator of terms
yield 1
for n in count(1):
d = factorint(n)
k, l = sorted(d.keys()), len(d)
if l > 0 and l == primepi(max(d)):
for i in range(l // 2):
if d[k[i]] != d[k[l - i - 1]]:
break
else:
yield n
def A332517(n):
return sum(totient(d) * (n // d) ** n for d in divisors(n, generator=True))
def A006722_gen(): # generator of terms
blist = [1] * 6
yield from blist
while True:
blist = blist[1:] + [
(blist[-1] * blist[-5] + blist[-2] * blist[-4] + blist[-3] ** 2)
// blist[-6]
]
yield blist[-1]
def A008863(n):
return (
n
* (
n
* (
n
* (
n
* (
n
* (n * (n * (n * (n * (n - 35) + 600) - 5790) + 36813) - 140595)
+ 408050
)
- 382060
)
+ 1368936
)
+ 2342880
)
// 3628800
+ 1
)
def A011965_gen(): # generator of terms
yield 1
blist = [1, 2]
while True:
blist = list(accumulate([blist[-1]] + blist))
yield blist[-3]
def A034302_gen(): # generator of terms
yield from [23, 37, 53, 73]
for l in count(1):
for d in product("123456789", repeat=l):
for e in product("1379", repeat=2):
s = "".join(d + e)
if isprime(int(s)):
for i in range(len(s)):
if not isprime(int(s[:i] + s[i + 1 :])):
break
else:
yield int(s)
def A036953_gen():
return filter(isprime, (int(gmpy2digits(n, 3)) for n in count(0)))
def A054683_gen(startvalue=0):
return filter(
lambda i: not sum(int(d) for d in str(i)) % 2, count(max(startvalue, 0))
)
def A064538(n):
p, m = 2, n + 1
while p <= (n + 2) // (2 + (n % 2)):
if sum(d for d in sympydigits(n + 1, p)[1:]) >= p:
m *= p
p = nextprime(p)
return m
def A066321(n):
if n == 0:
return 0
else:
s, q = "", n
while q:
q, r = c_divmod(q, -4)
s += ("0000", "1000", "0011", "1011")[r]
return int(s[::-1], 2)
@lru_cache(maxsize=None)
def A082540(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A082540(k1)
j, k1 = j2, n // j2
return n * (n**3 - 1) - c + j
def A087116(n):
return sum(1 for d in bin(n)[2:].split("1") if len(d))
def A096825(n):
fs = factorint(n)
return len(list(multiset_combinations(fs, sum(fs.values()) // 2)))
@lru_cache(maxsize=None)
def A100448(n):
if n == 0:
return 0
c, j = 2, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (6 * A100448(k1) + 1)
j, k1 = j2, n // j2
return (n * (n**2 - 1) - c + j) // 6
def A129135_gen(): # generator of terms
m, x = 1, 0
for n in count(5):
x, m = x * n + m * comb(n, 5), -m
yield x
def A187795(n):
return sum(d for d in divisors(n, generator=True) if divisor_sigma(d) > 2 * d)
def A246660(n):
return prod(factorial(len(d)) for d in split("0+", bin(n)[2:]) if d) if n > 0 else 1
def A256617_gen(startvalue=1):
return filter(
lambda n: len(plist := primefactors(n)) == 2
and plist[1] == nextprime(plist[0]),
count(max(startvalue, 1)),
)
def A272369_gen():
return filter(
lambda n: all(
(d in (1, 2, 4, 46) or not isprime(d + 1))
for d in divisors(n, generator=True)
),
count(92, 92),
)
def A317086(n):
if n > 3 and isprime(n):
return 1
else:
c = 1
for d in partitions(n, k=integer_nthroot(2 * n, 2)[0], m=n * 2 // 3):
l = len(d)
if l > 0:
k = max(d)
if l == k:
for i in range(k // 2):
if d[i + 1] != d[k - i]:
break
else:
c += 1
return c
def A331757(n):
return (
8
if n == 1
else 2
* (
n * (n + 3)
+ sum(totient(i) * (n + 1 - i) * (n + 1 + i) for i in range(2, n // 2 + 1))
+ sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i)
for i in range(n // 2 + 1, n + 1)
)
)
)
def A005351(n):
s, q = "", n
while q >= 2 or q < 0:
q, r = divmod(q, -2)
if r < 0:
q += 1
r += 2
s += str(r)
return int(str(q) + s[::-1], 2)
def A028909(n):
return int("".join(sorted(str(2**n))))
def A028910(n):
return int("".join(sorted(str(2**n), reverse=True)))
def A039723(n):
s, q = "", n
while q >= 10 or q < 0:
q, r = divmod(q, -10)
if r < 0:
q += 1
r += 10
s += str(r)
return int(str(q) + s[::-1])
def A055685_gen(startvalue=2):
return filter(lambda n: pow(2, n, n - 1) == n - 2, count(max(startvalue, 2)))
def A065712(n):
return str(2**n).count("1")
def A067388_gen(): # generator of terms
p = 2
q, r, s = p + 48, p + 96, p + 144
while True:
np = nextprime(p)
if (
np == q
and isprime(r)
and isprime(s)
and nextprime(q) == r
and nextprime(r) == s
):
yield p
p, q, r, s = np, np + 48, np + 96, np + 144
def A075101(n):
return (Fraction(2**n) / n).numerator
@lru_cache(maxsize=None)
def A090025(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A090025(k1)
j, k1 = j2, n // j2
return (n + 1) ** 3 - c + 7 * (j - n - 1)
def A350153_gen():
return filter(
lambda p: isprime(p),
(
int(s)
for n in count(1)
for s in accumulate(
str(d) for d in chain(range(1, n + 1), range(n - 1, 0, -1))
)
),
)
def A259937(n):
return int("".join(str(d) for d in chain(range(1, n + 1), range(n, 0, -1))))
def A350233_gen(startvalue=1):
return filter(
lambda n: (m := int(str(n)[::-1])) % 5 and not m % 4,
filter(lambda n: n % 4 and not n % 5, count(max(startvalue, 1))),
)
def A350232_gen(startvalue=1):
return filter(
lambda n: (m := int(str(n)[::-1])) % 4 and not m % 5,
filter(lambda n: n % 5 and not n % 4, count(max(startvalue, 1))),
)
def A350228_gen():
yield from (1, 0)
b, bdict = 0, {1: (1,), 0: (2,)}
for n in count(3):
if len(l := bdict[b]) > 1:
m = (n - 1 - l[-2]) * b
if m in bdict:
bdict[m] = (bdict[m][-1], n)
else:
bdict[m] = (n,)
b = m
else:
bdict[1] = (bdict[1][-1], n)
b = 1
yield b
def A171918_gen(): # generator of terms
yield 8
b, bdict = 8, {8: (1,)}
for n in count(2):
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
yield b
def A171917_gen(): # generator of terms
b, bdict = 7, {7: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A171916_gen(): # generator of terms
b, bdict = 6, {6: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A171915_gen(): # generator of terms
b, bdict = 5, {5: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A171914_gen(): # generator of terms
b, bdict = 4, {4: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A171913_gen(): # generator of terms
b, bdict = 3, {3: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A171912_gen(): # generator of terms
b, bdict = 2, {2: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A171911_gen(): # generator of terms
b, bdict = 1, {1: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 0
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A181391_gen(): # generator of terms
b, bdict = 0, {0: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
else:
b = 0
bdict[0] = (bdict[0][-1], n)
def A309363_gen(): # generator of terms
b, bdict = 0, {0: (1,)}
for n in count(2):
yield b
if len(l := bdict[b]) > 1:
b = n - 1 - l[-2]
else:
b = 2
if b in bdict:
bdict[b] = (bdict[b][-1], n)
else:
bdict[b] = (n,)
def A092221_gen(startvalue=0):
return filter(lambda n: not bernoulli(2 * n).p % 59, count(max(startvalue, 0)))
def A281502_gen(startvalue=0):
return filter(lambda n: not bernoulli(2 * n).p % 691, count(max(startvalue, 0)))
def A100208_gen(): # generator of terms
xset, a = {1}, 1
yield a
while True:
a, b = 1, 1 + a**2
while not isprime(b) or a in xset:
b += 2 * a + 1
a += 1
xset.add(a)
yield a
def A349731(n):
return -1 if n == 0 else -((-n) ** n) * ff(Fraction(1, n), n)
def A109890_gen(): # generator of terms
yield from [1, 2]
s, y, b = 3, 3, set()
while True:
for i in divisors(s, generator=True):
if i >= y and i not in b:
yield i
s += i
b.add(i)
while y in b:
b.remove(y)
y += 1
break
def A110751_gen(startvalue=1):
return filter(
lambda n: primefactors(n) == primefactors(int(str(n)[::-1])),
count(max(startvalue, 1)),
)
def A112822(n):
k, l, h = 1, 1, Fraction(1, 1)
while l != h.denominator * (2 * n - 1):
k += 1
l = lcm(l, k)
h += Fraction(1, k)
return k
def A115005(n):
return (n - 1) * (2 * n - 1) + sum(
totient(i) * (n - i) * (2 * n - i) for i in range(2, n)
)
def A115920_gen(startvalue=1):
return filter(
lambda n: sorted(str(divisor_sigma(n))) == sorted(str(n)),
count(max(startvalue, 1)),
)
def A115921_gen(startvalue=1):
return filter(
lambda n: sorted(str(totient(n))) == sorted(str(n)), count(max(startvalue, 1))
)
def A153671_gen(): # generator of terms
n, k, q = 101, 100, 0
for m in count(1):
r = n % k
if r > q:
q = r
yield m
n *= 101
k *= 100
q *= 100
def A215728(n):
l, x = [str(d) * n for d in range(10)], 1
for m in count(0):
s = str(x)
for k in l:
if k in s:
return m
x *= 5
def A215729(n):
l, x = [str(d) * n for d in range(10)], 1
for m in count(0):
s = str(x)
for k in l:
if k in s:
return m
x *= 6
def A215730(n):
l, x = [str(d) * n for d in range(10)], 1
for m in count(0):
s = str(x)
for k in l:
if k in s:
return m
x *= 7
def A215733(n):
l, x = [str(d) * n for d in range(10)], 1
while True:
s = str(x)
for k in range(10):
if l[k] in s:
return k
x *= 3
def A260273_gen(): # generator of terms
yield 1
a = 1
while True:
b, s = 1, format(a, "b")
while format(b, "b") in s:
b += 1
a += b
s = format(a, "b")
yield a
def A331776(n):
return (
4
if n == 1
else 20 * n * (n - 1)
+ 4 * sum(totient(i) * (n + 1 - i) * (2 * n + 2 - i) for i in range(2, n + 1))
)
def A003128_gen(): # generator of terms
blist, a, b = [1], 1, 1
while True:
blist = list(accumulate([b] + blist))
c = blist[-1]
yield (c + a - 3 * b) // 2
a, b = b, c
def A048701(n):
return int((s := bin(n - 1)[2:]) + s[::-1], 2)
def A049479(n):
return min(factorint(2**n - 1))
def A061040(n):
return 9 * n**2 // gcd(n**2 - 9, 9 * n**2)
def A064614(n):
return (
prod((5 - p if 2 <= p <= 3 else p) ** e for p, e in factorint(n).items())
if n > 1
else n
)
def A065715(n):
return str(2**n).count("4")
def A065719(n):
return str(2**n).count("8")
def A072960_gen():
return chain(
[0],
(
int(a + "".join(b))
for l in count(0)
for a in "3689"
for b in product("03689", repeat=l)
),
)
@lru_cache(maxsize=None)
def A100449(n):
if n == 0:
return 1
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * ((A100449(k1) - 3) // 2)
j, k1 = j2, n // j2
return 2 * (n * (n - 1) - c + j) + 1
def A127936_gen(startvalue=1):
return filter(lambda i: isprime(int("01" * i + "1", 2)), count(max(startvalue, 1)))
def A171901is_ok(n):
s = str(n)
return any(s[i] == s[i - 1] for i in range(1, len(s)))
def A171901_gen(startvalue=0):
return filter(A171901is_ok, count(max(startvalue, 0)))
def A215731(n):
l, x = [str(d) * n for d in range(10)], 1
for m in count(0):
s = str(x)
for k in l:
if k in s:
return m
x *= 11
def A215737(n):
a, s = 1, tuple(str(i) * n for i in range(10))
while True:
a *= 11
t = str(a)
for i, x in enumerate(s):
if x in t:
return i
def A230625(n):
return (
1
if n == 1
else int(
"".join(
[bin(y)[2:] for x in sorted(factorint(n).items()) for y in x if y != 1]
),
2,
)
)
def A237600_gen(startvalue=2): # generator of terms
n = max(nextprime(startvalue - 1), 2)
while True:
s = format(n, "x")
for i in range(1, len(s)):
if not is_prime(int(s[:-i], 16)):
break
else:
yield n
n = nextprime(n)
def A252648_gen(): # generator of terms
yield 1
for m in count(1):
l, L, dm, xlist, q = 1, 1, [d**m for d in range(10)], [0], 9**m
while l * q >= L:
for c in combinations_with_replacement(range(1, 10), l):
n = sum(dm[d] for d in c)
if sorted(int(d) for d in str(n)) == [0] * (
len(str(n)) - len(c)
) + list(c):
xlist.append(n)
l += 1
L *= 10
yield from sorted(xlist)
def A272695(n):
return int((n * sin(n)).round())
def A000790(n):
c = 4
while pow(n, c, c) != (n % c) or isprime(c):
c += 1
return c
def A008281_gen(): # generator of terms
blist = [1]
while True:
yield from blist
blist = [0] + list(accumulate(reversed(blist)))
@lru_cache(maxsize=None)
def A015631(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A015631(k1)
j, k1 = j2, n // j2
return n * (n - 1) * (n + 4) // 6 - c + j
def A046447_gen(): # generator of terms
yield 1
m = 4
while True:
k = nextprime(m)
for n in range(m, k):
if (
s := "".join([str(p) * e for p, e in sorted(factorint(n).items())])
) == s[::-1]:
yield n
m = k + 1
def A057708_gen(): # generator of terms
m = 2
for k in count(1):
if isprime(int(str(m)[::-1])):
yield k
m *= 2
def A063454(n):
ndict = {}
for i in range(n):
m = pow(i, 3, n)
if m in ndict:
ndict[m] += 1
else:
ndict[m] = 1
count = 0
for i in ndict:
ni = ndict[i]
for j in ndict:
k = (i + j) % n
if k in ndict:
count += ni * ndict[j] * ndict[k]
return count
def A350244_gen():
yield 1
k, b, bdict = 1, 0, {1: (1,), 0: (2,)}
for n in count(3):
if len(l := bdict[b]) > 1:
m = (n - 1 - l[-2]) * b
if m in bdict:
bdict[m] = (bdict[m][-1], n)
else:
bdict[m] = (n,)
b = m
else:
bdict[1] = (bdict[1][-1], n)
b = 1
if b > k:
k = b
yield n
def A069942_gen(startvalue=1):
return filter(
lambda n: sum(map(lambda x: int(str(x)[::-1]) if x < n else 0, divisors(n)))
== int(str(n)[::-1]),
count(max(startvalue, 1)),
)
def A071869_gen(): # generator of terms
p, q, r = 1, 2, 3
for n in count(2):
p, q, r = q, r, max(factorint(n + 2))
if p < q < r:
yield n
def A071870_gen(): # generator of terms
p, q, r = 1, 2, 3
for n in count(2):
p, q, r = q, r, max(factorint(n + 2))
if p > q > r:
yield n
def A076197_gen(): # generator of terms
g = 1
for i in count(3, 2):
g *= i
if is_prime(g + 1024):
yield i
@lru_cache(maxsize=None)
def A090026(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A090026(k1)
j, k1 = j2, n // j2
return (n + 1) ** 4 - c + 15 * (j - n - 1)
@lru_cache(maxsize=None)
def A090027(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A090027(k1)
j, k1 = j2, n // j2
return (n + 1) ** 5 - c + 31 * (j - n - 1)
@lru_cache(maxsize=None)
def A090028(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A090028(k1)
j, k1 = j2, n // j2
return (n + 1) ** 6 - c + 63 * (j - n - 1)
@lru_cache(maxsize=None)
def A090029(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A090029(k1)
j, k1 = j2, n // j2
return (n + 1) ** 7 - c + 127 * (j - n - 1)
def A114146(n):
return (
1
if n == 0
else 8 * n**2
- 12 * n
+ 6
+ 4 * sum(totient(i) * (n - i) * (2 * n - i) for i in range(2, n))
)
def A153679_gen(): # generator of terms
n, k, q = 1024, 1000, 0
for m in count(1):
r = n % k
if r > q:
q = r
yield m
n *= 1024
k *= 1000
q *= 1000
def A166374_gen(startvalue=1):
return filter(
lambda n: sum([int(n * e / p) for p, e in factorint(n).items()]) == totient(n),
count(max(startvalue, 1)),
)
def A350253(n):
return (
1
if (m := n % 6) == 2 or m == 5
else (fibonacci(n + 1) if m == 3 else fibonacci(n))
)
def A195269(n):
m, s = 1, "0" * n
for i in count(1):
m *= 3
if s in str(m):
return i
def A230891_gen(): # generator of terms
yield from [0, 11]
l, s, b = Counter("11"), 1, {3}
while True:
i = s
while True:
if i not in b:
li, o = Counter(bin(i)[2:]), 0
for d in (l + li).values():
if d % 2:
if o > 0:
break
o += 1
else:
yield int(bin(i)[2:])
l = li
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A245562_gen(): # generator of terms
yield 0
for n in count(1):
yield from (len(d) for d in split("0+", bin(n)[2:]) if d != "")
def A247648_gen(startvalue=1):
return filter(lambda n: n % 2 and not "00" in bin(n), count(max(startvalue, 1)))
def A274086(n):
return int((n * tan(n)).round())
def A274087(n):
return int((n**2 * sin(n)).round())
def A274088(n):
return int((n**2 * sin(sqrt(n))).round())
def A274090(n):
return int((n**2 * cos(sqrt(n))).round())
def A274091(n):
k, j = divmod(n, 2)
return int((k**2 * sin(sqrt(k) + j * pi / 2)).round())
def A274092(n):
k, j = divmod(n, 3)
return int((k**2 * sin(sqrt(k) + j * pi / 2)).round())
def A274095(n):
return int((n * sin(sqrt(n))).round())
def A274097(n):
k, j = divmod(n, 3)
return int((k * sin(sqrt(k) + j * pi / 2)).round())
def A317085(n):
c = 1
for d in partitions(n, m=n * 2 // 3):
l = len(d)
if l > 0:
k = sorted(d.keys())
for i in range(l // 2):
if d[k[i]] != d[k[l - i - 1]]:
break
else:
c += 1
return c
def A320485(n):
return (lambda x: int(x) if x != "" else -1)(
"".join(d if str(n).count(d) == 1 else "" for d in str(n))
)
def A328095_gen(startvalue=0):
return filter(
lambda n: (sn := str(n)) in str(n * prod(int(d) for d in sn)),
count(max(startvalue, 0)),
)
def A337856(n):
k, n1, n2, pset = 0, 10 ** (n - 1) // 2 - 18, 10**n // 2 - 18, set()
while 50 * k**2 + 60 * k < n2:
a, b = divmod(n1 - 30 * k, 50 * k + 30)
m = max(k, a + int(b > 0))
r = 50 * k * m + 30 * (k + m)
while r < n2:
pset.add(r)
m += 1
r += 50 * k + 30
k += 1
return len(pset)
def A345687(n):
return pvariance(
n**2 * u
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A003512(n):
return 2 * n + int(isqrt(3 * n**2))
def A004720(n):
l = len(str(n - 1))
m = (10**l - 1) // 9
k = n + l - 2 + int(n + l - 1 >= m)
return 0 if k == m else int(str(k).replace("1", ""))
def A005487_gen(): # generator of terms
blist, bset = [0, 4], {0, 4}
yield from blist
for i in count(0):
n, flag = blist[-1] + 1, False
while True:
for j in range(i + 1, 0, -1):
m = 2 * blist[j] - n
if m in bset:
break
if m < 0:
flag = True
break
else:
blist.append(n)
bset.add(n)
yield n
break
if flag:
blist.append(n)
bset.add(n)
yield n
break
n += 1
def A006723_gen(): # generator of terms
blist = [1] * 7
yield from blist
while True:
blist = blist[1:] + [
(blist[-1] * blist[-6] + blist[-2] * blist[-5] + blist[-3] * blist[-4])
// blist[-7]
]
yield blist[-1]
def A007487(n):
return (
n**2
* (n**2 * (n**2 * (n**2 * (n * (2 * n + 10) + 15) - 14) + 10) - 3)
// 20
)
def A008559_gen(): # generator of terms
b = 2
while True:
yield b
b = int(bin(b)[2:])
def A027602(n):
return n * (n * (3 * n + 9) + 15) + 9
def A029976_gen():
return filter(isprime, pal_gen(8))
def A029997_gen():
return filter(
lambda n: gmpy2digits(n, 11) == gmpy2digits(n, 11)[::-1],
(n**2 for n in count(0)),
)
def A036967_gen(startvalue=1):
return filter(
lambda n: min(factorint(n).values(), default=4) >= 4, count(max(startvalue, 1))
)
def A048543(n):
k, m = 1, 2
while True:
if str(m).count("7") == n:
return k
k += 1
m += 2 * k
def A048544(n):
k, m = 1, 2
while True:
if str(m).count("7") == n:
return m
k += 1
m += 2 * k
def A053165(n):
return 1 if n <= 1 else prod(p ** (e % 4) for p, e in factorint(n).items())
def A054383_gen(): # generator of terms
l = {}
for d in permutations("123456789", 9):
for i in range(8):
s1, s2 = int("".join(d[: i + 1])), int("".join(d[i + 1 :]))
q, r = divmod(s1, s2)
if not r:
if q in l:
l[q] += 1
else:
l[q] = 1
for i in count(1):
if i in l:
yield l[i]
else:
yield 0
def A055155(n):
return sum(gcd(d, n // d) for d in divisors(n, generator=True))
def A058411_gen(startvalue=0):
return filter(
lambda i: i % 10 and max(str(i**2)) < "3", count(max(startvalue, 0))
)
def A064834(n):
x, y = str(n), 0
lx2, r = divmod(len(x), 2)
for a, b in zip(x[:lx2], x[: lx2 + r - 1 : -1]):
y += abs(int(a) - int(b))
return y
def A065714(n):
return str(2**n).count("3")
def A065716(n):
return str(2**n).count("5")
def A065717(n):
return str(2**n).count("6")
def A065718(n):
return str(2**n).count("7")
def A065744(n):
return str(2**n).count("9")
def A073785(n):
s, q = "", n
while q >= 3 or q < 0:
q, r = divmod(q, -3)
if r < 0:
q += 1
r += 3
s += str(r)
return int(str(q) + s[::-1])
def A073786(n):
s, q = "", n
while q >= 5 or q < 0:
q, r = divmod(q, -5)
if r < 0:
q += 1
r += 5
s += str(r)
return int(str(q) + s[::-1])
def A073787(n):
s, q = "", n
while q >= 6 or q < 0:
q, r = divmod(q, -6)
if r < 0:
q += 1
r += 6
s += str(r)
return int(str(q) + s[::-1])
def A073788(n):
s, q = "", n
while q >= 7 or q < 0:
q, r = divmod(q, -7)
if r < 0:
q += 1
r += 7
s += str(r)
return int(str(q) + s[::-1])
def A073789(n):
s, q = "", n
while q >= 8 or q < 0:
q, r = divmod(q, -8)
if r < 0:
q += 1
r += 8
s += str(r)
return int(str(q) + s[::-1])
def A073790(n):
s, q = "", n
while q >= 9 or q < 0:
q, r = divmod(q, -9)
if r < 0:
q += 1
r += 9
s += str(r)
return int(str(q) + s[::-1])
def A066417(n):
return (
0
if n == 1
else divisor_sigma(2 * n - 1)
+ divisor_sigma(2 * n + 1)
+ divisor_sigma(n // 2 ** (k := multiplicity(2, n))) * 2 ** (k + 1)
- 6 * n
- 2
)
def A073930_gen(startvalue=2):
return filter(
lambda n: divisor_sigma(2 * n - 1)
+ divisor_sigma(2 * n + 1)
+ divisor_sigma(n // 2 ** (k := multiplicity(2, n))) * 2 ** (k + 1)
- 7 * n
- 2
== 0,
count(max(startvalue, 2)),
)
def A192268_gen(startvalue=2):
return filter(
lambda n: divisor_sigma(2 * n - 1)
+ divisor_sigma(2 * n + 1)
+ divisor_sigma(n // 2 ** (k := multiplicity(2, n))) * 2 ** (k + 1)
- 7 * n
- 2
> 0,
count(max(startvalue, 2)),
)
def A082410(n):
if n == 1:
return 0
s = bin(n - 1)[2:]
m = len(s)
i = s[::-1].find("1")
return 1 - int(s[m - i - 2]) if m - i - 2 >= 0 else 1
def A111116_gen(startvalue=1):
return filter(
lambda n: len(set(str(n)) & set(str(n**4))) == 0, count(max(startvalue, 1))
)
def A115927_gen(): # generator of terms
l = {}
for d in permutations("0123456789", 10):
if d[0] != "0":
for i in range(9):
if d[i + +1] != "0":
q, r = divmod(int("".join(d[: i + 1])), int("".join(d[i + 1 :])))
if not r:
if q in l:
l[q] += 1
else:
l[q] = 1
for i in count(1):
if i in l:
yield l[i]
else:
yield 0
def A235811_gen(startvalue=0):
return filter(lambda n: len(set(str(n**3))) == 9, count(max(startvalue, 0)))
def A235809_gen(startvalue=0):
return filter(lambda n: len(set(str(n**3))) == 7, count(max(startvalue, 0)))
def A137921(n):
return len([d for d in divisors(n, generator=True) if n % (d + 1)])
def A153686_gen(): # generator of terms
k10, k11 = 10, 11
for k in count(1):
if (k11 % k10) * k < k10:
yield k
k10 *= 10
k11 *= 11
def A153670_gen(): # generator of terms
k10, k11 = 100, 101
for k in count(1):
if (k11 % k10) * k < k10:
yield k
k10 *= 100
k11 *= 101
def A153687_gen(): # generator of terms
n, k, q = 11, 10, 0
for m in count(1):
r = n % k
if r > q:
q = r
yield m
n *= 11
k *= 10
q *= 10
def A177029_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
n, c = 3, 0
while n * (n + 1) <= 2 * m:
if not 2 * (n * (n - 2) + m) % (n * (n - 1)):
c += 1
if c > 1:
break
n += 1
if c == 1:
yield m
def A187824(n):
k = 1
while (n + 1) % k < 3:
k += 1
return k - 1
def A206709(n):
c, b, b2, n10 = 0, 1, 2, 10**n
while b <= n10:
if isprime(b2):
c += 1
b += 1
b2 += 2 * b - 1
return c
def A219531(n):
return (
n
* (
n
* (
n
* (
n
* (
n
* (
n
* (
n * (n * (n * (n * (n - 44) + 935) - 11550) + 94083)
- 497112
)
+ 1870385
)
- 3920950
)
+ 8550916
)
+ 4429656
)
+ 29400480
)
// 39916800
+ 1
)
def A226561(n):
return sum(totient(d) * d**n for d in divisors(n, generator=True))
def A228640(n):
return sum(totient(d) * n ** (n // d) for d in divisors(n, generator=True))
def A242171_gen(): # generator of terms
yield 1
bell_list, blist, b = [1, 1], [1], 1
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
fs = primefactors(b)
for p in fs:
if all(n % p for n in bell_list):
yield p
break
else:
yield 1
bell_list.append(b)
def A245563_gen():
yield from chain(
[0], (len(d) for n in count(1) for d in split("0+", bin(n)[:1:-1]) if d != "")
)
def A246588(n):
return (
prod(bin(len(d)).count("1") for d in split("0+", bin(n)[2:]) if d)
if n > 0
else 1
)
def A246595(n):
return prod(len(d) ** 2 for d in split("0+", bin(n)[2:]) if d != "") if n > 0 else 1
def A246596(n):
s, c = bin(n)[2:], [1, 1]
for m in range(1, len(s)):
c.append(c[-1] * (4 * m + 2) // (m + 2))
return prod(c[len(d)] for d in split("0+", s)) if n > 0 else 1
def A247649_gen(): # generator of terms
from sympy.abc import x
f, g, blist = 1 / x**2 + 1 / x + 1 + x + x**2, 1, [1]
yield 1
for n in count(1):
s = [int(d, 2) for d in bin(n)[2:].split("00") if d != ""]
g = (g * f).expand(modulus=2)
if len(s) == 1:
blist.append(g.subs(x, 1))
yield blist[-1]
else:
blist.append(prod(blist[d] for d in s))
yield blist[-1]
def A225654_gen(): # generator of terms
from sympy.abc import x
f, g, blist, c = 1 / x**2 + 1 / x + 1 + x + x**2, 1, [1], 1
yield c
for n in count(1):
s = [int(d, 2) for d in bin(n)[2:].split("00") if d != ""]
g = (g * f).expand(modulus=2)
if len(s) == 1:
blist.append(g.subs(x, 1))
else:
blist.append(prod(blist[d] for d in s))
c += blist[-1]
yield c
def A254449(n):
if n == 0:
return 0
i, m, s = 1, 1, "4" * n
s2 = s + "4"
while True:
m *= i
sn = str(m)
if s in sn and s2 not in sn:
return i
i += 1
def A266142(n):
return (
4 * n
if (n == 1 or n == 2)
else sum(
1
for d in range(-3, 7)
for i in range(n)
if isprime((10**n - 1) // 3 + d * 10**i)
)
)
def A266146(n):
return (
4 * n
if (n == 1 or n == 2)
else sum(
1
for d in range(-7, 3)
for i in range(n)
if isprime(7 * (10**n - 1) // 9 + d * 10**i)
)
)
def A266148(n):
return sum(
1 for d in range(-9, 1) for i in range(n) if isprime(10**n - 1 + d * 10**i)
)
def A289673_gen():
return (
-1 if s == ("1",) else int(("".join(s) + ("2212" if s[0] == "2" else "11"))[3:])
for l in count(1)
for s in product("12", repeat=l)
)
def A305611(n):
fs = factorint(n)
return len(
set(
sum(d)
for i in range(1, sum(fs.values()) + 1)
for d in multiset_combinations(fs, i)
)
)
def A317088(n):
if n == 0:
return 1
c = 0
for d in partitions(n, k=isqrt(2 * n)):
l = len(d)
if l > 0 and l == max(d):
v = set(d.values())
if len(v) == max(v):
c += 1
return c
def A345688(n):
return pvariance(
n**2 * v
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A004721(n):
l = len(str(n))
m = 2 * (10**l - 1) // 9
k = n + l - int(n + l < m)
return 1 if k == m else int(str(k).replace("2", ""))
def A004722(n):
l = len(str(n))
m = (10**l - 1) // 3
k = n + l - int(n + l < m)
return 2 if k == m else int(str(k).replace("3", ""))
def A004724(n):
l = len(str(n))
m = 5 * (10**l - 1) // 9
k = n + l - int(n + l < m)
return 4 if k == m else int(str(k).replace("5", ""))
def A004731(n):
if n <= 1:
return 1
a, b = factorial2(n - 2), factorial2(n - 1)
return b // gcd(a, b)
def A011968_gen(): # generator of terms
yield from [1, 2]
blist, b = [1], 1
while True:
blist = list(accumulate([b] + blist))
yield b + blist[-1]
b = blist[-1]
def A014710(n):
s = bin(n + 1)[2:]
m = len(s)
i = s[::-1].find("1")
return 2 - int(s[m - i - 2]) if m - i - 2 >= 0 else 2
def A017713_gen(): # generator of terms
m = [1] * 50
while True:
yield m[-1]
for i in range(49):
m[i + 1] += m[i]
def A017713(n):
return comb(n, 49)
def A020462_gen():
return filter(
isprime, (int("".join(x)) for n in count(1) for x in product("35", repeat=n))
)
@lru_cache(maxsize=None)
def A022825(n):
if n <= 1:
return n
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A022825(k1)
j, k1 = j2, n // j2
return c + n + 1 - j
def A030665(n):
d, nd = 10, 10 * n
while True:
x = nextprime(nd)
if x < nd + d:
return int(x)
d *= 10
nd *= 10
def A050932(n):
return (q := bernoulli(n).q) // gcd(q, n + 1)
def A053600_gen(): # generator of terms
yield 2
p = 2
while True:
m, ps = 1, str(p)
s = int("1" + ps + "1")
while not isprime(s):
m += 1
ms = str(m)
s = int(ms + ps + ms[::-1])
p = s
yield p
def A054268_gen():
return filter(
lambda p: len(set(str(int(((q := nextprime(p)) - p - 1) * (q + p) // 2)))) == 1,
(prime(n) for n in count(2)),
)
def A061308_gen(): # generator of terms
for n in count(2, 2):
p = prevprime((n3 := n**3) // 2)
if p + nextprime(p) == n3:
yield p
def A061783_gen():
return filter(
lambda p: isprime(p + int(str(p)[::-1])), (prime(n) for n in count(1))
)
@lru_cache(maxsize=None)
def A063985(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (k1 * (k1 + 1) - 2 * A063985(k1) - 1)
j, k1 = j2, n // j2
return (2 * n + c - j) // 2
def A065847(n):
return max(
sum(
1
for t in multiset_permutations(s)
if t[0] != "0" and isprime(int("".join(t), 6))
)
for s in combinations_with_replacement("012345", n)
)
def A069862(n):
nk, kr, r = n + 1, 1, 1 if n > 1 else 0
while r:
nk += 1
kr = (kr + 1) % n
r = (r * (10 ** len(str(nk)) % n) + kr) % n
return nk - n
def A074989(n):
a = integer_nthroot(n, 3)[0]
return min(n - a**3, (a + 1) ** 3 - n)
def A082491_gen(): # generator of terms
m, x = 1, 1
for n in count(0):
x, m = x * n**2 + m, -(n + 1) * m
yield x
def A087666(n):
c, x = 0, n
a, b = divmod(x, 3)
while b != 0:
x *= a
c += 1
a, b = divmod(x, 3)
return c
def A088658(n):
return 4 * (n - 1) ** 2 + 4 * sum(
totient(i) * (n - i) * (2 * n - i) for i in range(2, n)
)
def A091049(n):
k = 1
while True:
m1 = k
for i in range(n + 1):
m2 = int(str(m1), 1 + max(int(d) for d in str(m1)))
if m1 == m2:
if i == n:
return k
else:
break
m1 = m2
k += 1
def A094577_gen(): # generator of terms
yield 1
blist, b = [1], 1
for n in count(2):
blist = list(accumulate([b] + blist))
b = blist[-1]
blist = list(accumulate([b] + blist))
b = blist[-1]
yield blist[-n]
def A094519_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
for i in range(1, len(d := divisors(n))):
di = d[i]
for j in range(i):
if n % (di + d[j]) == 0:
yield n
break
else:
continue
break
def A095149_gen(): # generator of terms
yield from [1] * 3
blist = [1]
while True:
blist = list(accumulate([blist[-1]] + blist))
yield blist[-1]
yield from blist
def A097227_gen(): # generator of terms
ptuple = (2, 3, 5, 7, 11, 13, 17, 19, 23)
for l in count(1):
for d in combinations_with_replacement(range(1, 10), l):
if (n := prod(ptuple[i - 1] for i in d)) < 10 ** l and tuple(
sorted((int(x) for x in str(n)))
) == d:
yield n
def A102487(n):
return int(str(n), 12)
def A102491(n):
return int(str(n), 20)
def A007091(n):
return int(gmpy2digits(n, 5))
def A131535(n):
s, t, m, k, u = "1" * n, "1" * (n + 1), 0, 1, "1"
while s not in u or t in u:
m += 1
k *= 2
u = str(k)
return m
def A131544(n):
m, s = 1, "9" * n
for i in count(1):
m *= 3
if s in str(m):
return i
def A131546(n):
str7 = "7" * n
x, exponent = 3, 1
while not str7 in str(x):
exponent += 1
x *= 3
return exponent
def A131552(n):
m, s = 1, "1" * n
for i in count(1):
m *= 3
if s in str(m):
return i
def A153695_gen(): # generator of terms
m10, m9, q = 10, 9, 0
for m in count(1):
r = m10 % m9
if r > q:
q = r
yield m
m10 *= 10
m9 *= 9
q *= 9
def A153745_gen(): # generator of terms
for l in count(1):
if not is_prime(l):
fs = divisors(l)
a = isqrt(10 ** (l - 1)) + ((l - 1) % 2)
for n in range(a, isqrt(10**l - 1) + 1):
for g in fs:
if not is_square(
sum(int(str(n**2)[h : h + g]) for h in range(0, l, g))
):
break
else:
yield n
def A155146_gen(): # generator of terms
n3, m = 0, 0
for n in count(1):
m += 6 * (n - 1)
n3 += m + 1
if len(set(str(n3))) == 3:
yield n
def A159065(n):
return (
n - 1
if n <= 2
else 2 * n
- 3
+ 3 * sum(totient(i) * (n - i) * i for i in range(2, (n + 1) // 2))
+ sum(totient(i) * (n - i) * (2 * n - i) for i in range((n + 1) // 2, n))
)
def A163573_gen():
return (
4 * q - 3
for q in (prime(i) for i in count(1))
if isprime(4 * q - 3)
and isprime(2 * q - 1)
and (not (4 * q - 1) % 3)
and isprime((4 * q - 1) // 3)
)
def A175047(n):
return int(
"".join(
d + "0" if "0" in d else d
for d in split("(0+)|(1+)", bin(n)[2:])
if d != "" and d != None
),
2,
)
def A188068(n):
return int(isqrt(3 * n**2) - isqrt(3 * (n - 1) ** 2)) - 1
def A201053(n):
return (
a**3
if 2 * n < (a := integer_nthroot(n, 3)[0]) ** 3 + (a + 1) ** 3
else (a + 1) ** 3
)
def A211264(n):
return (lambda m: sum(n // k for k in range(1, m + 1)) - m * (m + 1) // 2)(isqrt(n))
def A212529(n):
s, q = "", -n
while q >= 2 or q < 0:
q, r = divmod(q, -2)
if r < 0:
q += 1
r += 2
s += str(r)
return int(str(q) + s[::-1])
def A219327_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = [int(d) for d in str(n)]
m = len(s)
if n == abs(Matrix(m, m, lambda i, j: s[(i - j) % m]).det()):
yield n
def A230892_gen(): # generator of terms
yield from [0, 3]
l, s, b = Counter("11"), 1, {3}
while True:
i = s
while True:
if i not in b:
li, o = Counter(bin(i)[2:]), 0
for d in (l + li).values():
if d % 2:
if o > 0:
break
o += 1
else:
yield i
l = li
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A244112(n):
return int(
"".join([str(str(n).count(d)) + d for d in "9876543210" if str(n).count(d) > 0])
)
def A249915_gen(): # generator of terms
for l in count(0):
for a in product("23456", repeat=l):
for b in ("2", "4", "5", "6"):
s = "".join(a) + b
if "2" in s and "6" in s:
n = int(s)
if {"2", "6"} <= set(str(n**2)) <= {"2", "3", "4", "5", "6"}:
yield n
def A287055_gen(): # generator of terms
a = 1
for n in count(1):
b = prod(p**e - 1 for p, e in factorint(n + 1).items())
if a == b:
yield n
a, n = b, n + 1
def A296369_gen(startvalue=1):
return filter(lambda n: pow(2, n + 1, n) == n - 1, count(max(startvalue, 1)))
def A324043(n):
return (
0
if n == 1
else -2 * (n - 1) ** 2
+ sum(
totient(i) * (n + 1 - i) * (7 * i - 2 * n - 2) for i in range(2, n // 2 + 1)
)
+ sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i) for i in range(n // 2 + 1, n + 1)
)
)
def A335567(n):
return (n - (m := divisor_count(n))) * (n - m + 1) // 2
def A341715(n):
m, k = n, n
while not isprime(m):
k += 1
m = int(str(m) + str(k))
return m
def A345689(n):
return pvariance(
n**2 * abs(u)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A003221_gen(): # generator terms
m, x = -1, 0
for n in count(0):
x, m = x * n + m * (n * (n - 1) // 2 - 1), -m
yield x
def A004723(n):
l = len(str(n))
m = 4 * (10**l - 1) // 9
k = n + l - int(n + l < m)
return 3 if k == m else int(str(k).replace("4", ""))
def A004725(n):
l = len(str(n))
m = 2 * (10**l - 1) // 3
k = n + l - int(n + l < m)
return 5 if k == m else int(str(k).replace("6", ""))
def A004726(n):
l = len(str(n))
m = 7 * (10**l - 1) // 9
k = n + l - int(n + l < m)
return 6 if k == m else int(str(k).replace("7", ""))
def A004727(n):
l = len(str(n))
m = 8 * (10**l - 1) // 9
k = n + l - int(n + l < m)
return 7 if k == m else int(str(k).replace("8", ""))
def A007464_gen(): # generator of terms
blist = [1, 1]
yield from blist
for n in count(1):
blist.append(sum(gcd(blist[i], blist[n - i]) for i in range(n + 1)))
yield blist[-1]
def A022488_gen(): # generator of terms
yield 2
l = "2"
while True:
l = "".join(
d[0] + str(len(d))
for d in split("(0+|1+|2+|3+|4+|5+|6+|7+|8+|9+)", l[::-1])
if d != ""
)
yield int(l)
def A047898_gen(): # generator of terms
l = 6
while True:
yield l
l *= sum(int(d) for d in str(l))
def A047901_gen(): # generator of terms
l = 9
while True:
yield l
l *= sum(int(d) for d in str(l))
def A059168_helper(w, dir):
if dir == 1:
for s in w:
for t in range(int(s[-1]) + 1, 10):
yield s + str(t)
else:
for s in w:
for t in range(0, int(s[-1])):
yield s + str(t)
def A059168_gen(): # generator of terms
for l in count(0):
for d in "123456789":
x = d
for i in range(1, l + 1):
x = A059168_helper(x, (-1) ** i)
yield from (int(p) for p in x if isprime(int(p)))
if l > 0:
y = d
for i in range(1, l + 1):
y = A059168_helper(y, (-1) ** (i + 1))
yield from (int(p) for p in y if isprime(int(p)))
def A061246_gen():
return (
int(i + "".join(j) + k)
for l in count(0)
for i in "149"
for j in product("0149", repeat=l)
for k in "19"
if isprime(int(i + "".join(j) + k))
)
def A063565(n):
s, k, k2 = str(n), 1, 2
while True:
if s in str(k2):
return k
k += 1
k2 *= 2
def A064169(n):
return (lambda x: x.p - x.q)(harmonic(n))
def A068187(n):
if n == 1:
return 1
pf = factorint(n)
return (
0
if max(pf) > 7
else int(
"".join(
sorted(
"".join(str(a) * (n * b) for a, b in pf.items())
.replace("222", "8")
.replace("22", "4")
.replace("33", "9")
)
)
)
)
def A072961_gen():
return (int("".join(a)) for l in count(1) for a in product("25", repeat=l))
def A081134(n):
kmin, kmax = 0, 1
while 3**kmax <= n:
kmax *= 2
while True:
kmid = (kmax + kmin) // 2
if 3**kmid > n:
kmax = kmid
else:
kmin = kmid
if kmax - kmin <= 1:
break
return min(n - 3**kmin, 3 * 3**kmin - n)
@lru_cache(maxsize=None)
def A082544(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A082544(k1)
j, k1 = j2, n // j2
return n * (n**4 - 1) - c + j
def A090709_gen():
return filter(isprime, (int(gmpy2digits(d, 6)) for d in count(0) if is_prime(d)))
def A091627(n):
m = isqrt(n)
return 0 if n == 0 else sum(n // k for k in range(1, m + 1)) - m * (m - 1) // 2 - 1
def A094593(n):
p = prime(n)
return 1 if n == 3 else (p - 1) // n_order(3, p)
def A118600_gen():
return palbase_gen(9)
def A118599_gen():
return palbase_gen(8)
def A118598_gen():
return palbase_gen(7)
def A118597_gen():
return palbase_gen(6)
def A118596_gen():
return palbase_gen(5)
def A118595_gen():
return palbase_gen(4)
def A118594_gen():
return palbase_gen(3)
def A123098(n):
return prod(1 if ~(n - 1) & k else prime(k + 1) for k in range(n))
def A131536(n):
s, t, m, k, u = "2" * n, "2" * (n + 1), 0, 1, "1"
while s not in u or t in u:
m += 1
k *= 2
u = str(k)
return m
def A145551_gen(startvalue=1):
return filter(
lambda n: not n ** divisor_sigma(n, 0) % divisor_sigma(n, 1) ** 2,
count(max(startvalue, 1)),
)
def A169639(n):
return sum(ord(s) - 96 for s in unidecode(num2words(n, lang="fr")) if s.isalpha())
def A189718_gen(): # generator of terms
blist = [0]
yield 0
while True:
x = [1 - d for d in blist] * 2
blist.extend(x)
yield from x
def A241100(n):
for i in range(1, 10):
x = i * (10**n - 1) // 9
for j in range(n - 1, -1, -1):
for k in range(i, -1, -1):
if j < n - 1 or k < i:
y = x - k * (10**j)
if isprime(y):
return y
for j in range(n):
for k in range(1, 9 - i + 1):
y = x + k * (10**j)
if isprime(y):
return y
def A266141(n):
return 4 if n == 1 else sum(1 for d in "1379" if isprime(int("2" * (n - 1) + d)))
def A266144(n):
return (
4
if n == 1
else sum(1 for d in [-4, -2, 2, 4] if isprime(5 * (10**n - 1) // 9 + d))
)
def A266145(n):
return (
4
if n == 1
else sum(1 for d in [-5, -3, 1, 3] if isprime(2 * (10**n - 1) // 3 + d))
)
def A266147(n):
return (
4
if n == 1
else sum(1 for d in [-7, -5, -1, 1] if isprime(8 * (10**n - 1) // 9 + d))
)
def A276740_gen(): # generator of terms
yield from [1, 2, 4]
yield from filter(lambda n: pow(3, n, n) == 5, count(5))
def A277289_gen(): # generator of terms
yield from [1, 2, 4, 5]
yield from filter(lambda n: pow(3, n, n) == n - 7, count(6))
def A277288_gen(): # generator of terms
yield from [1, 2]
yield from filter(lambda n: pow(3, n, n) == n - 5, count(3))
def A277340_gen(): # generator of terms
yield from [1, 2, 4, 7, 10]
yield from filter(lambda n: pow(3, n, n) == n - 11, count(11))
def A288104(n):
ndict = {}
for i in range(n):
m = pow(i, 9, n)
if m in ndict:
ndict[m] += 1
else:
ndict[m] = 1
count = 0
for i in ndict:
ni = ndict[i]
for j in ndict:
k = (i + j) % n
if k in ndict:
count += ni * ndict[j] * ndict[k]
return count
def A288105(n):
ndict = {}
for i in range(n):
m = pow(i, 10, n)
if m in ndict:
ndict[m] += 1
else:
ndict[m] = 1
count = 0
for i in ndict:
ni = ndict[i]
for j in ndict:
k = (i + j) % n
if k in ndict:
count += ni * ndict[j] * ndict[k]
return count
def A289677(n):
c, k, r, n2, cs, ts = (
0,
1 + (n - 1) // 3,
2 ** ((n - 1) % 3),
2 ** (n - 1),
set(),
set(),
)
for i in range(2**k):
j, l = int(bin(i)[2:], 8) * r, n2
traj = set([(l, j)])
while True:
if j >= l:
j = j * 16 + 13
l *= 2
else:
j *= 4
l //= 2
if l == 0:
ts |= traj
break
j %= 2 * l
if (l, j) in traj:
c += 1
cs |= traj
break
if (l, j) in cs:
c += 1
break
if (l, j) in ts:
break
traj.add((l, j))
return c
def A307371_gen(): # generator of terms
blist = [0, 1, 98, 99, 100, 9998]
yield from blist
while True:
blist = blist[1:] + [101 * blist[-3] - 100 * blist[-6]]
yield blist[-1]
def A307437(n):
for k in count(1):
if not reduced_totient(k) % (2 * n):
return k
def A324042(n):
return 2 * (
2 * n**2
- n
+ 1
+ 2
* sum(totient(i) * (n + 1 - 2 * i) * (n + 1 - i) for i in range(2, n // 2 + 1))
)
def A342632(n):
return 2 * sum(t for t in sieve.totientrange(1, 2**n + 1)) - 1
@lru_cache(maxsize=None)
def A343978(n):
if n == 0:
return 0
c, j, k1 = 1, 2, n // 2
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A343978(k1)
j, k1 = j2, n // j2
return n * (n**5 - 1) - c + j
def A344866(n):
return n * (n * (n * (2 * n - 11) + 23) - 21) + 7
def A345690(n):
return pvariance(
n**2 * abs(v)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A004728(n):
l = len(str(n))
m = 10**l - 1
k = n + l - int(n + l < m)
return 8 if k == m else int(str(k).replace("9", ""))
def A014957_gen(startvalue=1):
return filter(lambda n: n == 1 or pow(16, n, n) == 1, count(max(startvalue, 1)))
def A023002(n):
return (
n
* (
n**2
* (n**2 * (n**2 * (n**2 * (n * (6 * n + 33) + 55) - 66) + 66) - 33)
+ 5
)
// 66
)
def A160773_gen(): # generator of terms
p3, p5, p7 = [1] * 3
for k in count(0):
if isprime(p3 + p5 + p7):
yield k
p3 *= 3
p5 *= 5
p7 *= 7
def A349682(n):
return n * (n * (36 * n + 36) + 11) + 1
def A349466(n):
return 24 * 24**n + 64 * 2 ** (4 * n) - 81 * 18**n - 6 * 12**n
def A029455_gen(): # generator of terms
r = 0
for n in count(1):
r = r * 10 ** len(str(n)) + n
if not (r % n):
yield n
def A052045_gen(startvalue=1):
return filter(
lambda n: not str(n).count("0"), (n**3 for n in count(max(startvalue, 1)))
)
def A055941(n):
s = bin(n)[2:]
return sum(s[i:].count("0") for i, d in enumerate(s, start=1) if d == "1")
def A058233_gen(): # generator of terms
p, q, r = 2, 3, 2
while True:
if (r + 1) % q == 0:
yield p
r *= q
p, q = q, nextprime(q)
def A077110(n):
n2 = n**2
a = integer_nthroot(n2, 3)[0]
a2, a3 = a**3, (a + 1) ** 3
return a3 if a3 + a2 - 2 * n2 < 0 else a2
def A081762_gen():
return filter(
lambda p: pow(2, p - 1, p * (p - 2)) == 1, (prime(n) for n in count(2))
)
def A082216(n):
s = str(n)
t = s[::-1]
if s == t:
return n
for i in range(1, len(s)):
if s[i:] == t[:-i]:
return int(s + t[-i:])
def A085807(n):
return Matrix(n, n, [abs(j - k) for j in range(n) for k in range(n)]).per()
def A090287(n):
sn = str(n)
if n in (231, 420, 759) or not (len(sn) % 2 or n % 11):
return 0
for i in count(1):
for j in range(1, 10, 2):
si = str(j) * i
p = int(si + sn + si)
if isprime(p):
return p
def A099004_gen(): # generator of terms
yield 1
l, s, b1, b2 = 2, 3, set(), {1}
while True:
i = s
while True:
m = abs(i - l)
if not (i in b1 or m in b2):
yield i - l
b1.add(i)
b2.add(m)
l = i
while s in b1:
b1.remove(s)
s += 1
break
i += 1
def A110819_gen(startvalue=1):
return filter(
lambda n: (s := str(n)) != s[::-1]
and primefactors(n) == primefactors(int(s[::-1])),
count(max(startvalue, 1)),
)
def A111163_gen():
return filter(
lambda n: not isprime(n // 2) and prevprime(n // 2) + nextprime(n // 2) == n,
(n * (n + 1) // 2 for n in count(3)),
)
def A111234_gen():
return chain(
(2,), (a + b // a for a, b in ((min(factorint(n)), n) for n in count(2)))
)
def A124661_gen(): # generator of terms
for n in count(1):
p = prime(n)
for k in range(1, n - 1):
if prime(n - k) + prime(n + k) < 2 * p:
break
else:
yield p
def A127962_gen():
return (
int(bin(p)[2:])
for p in filter(isprime, ((2 ** prime(n) + 1) // 3 for n in count(2)))
)
def A145642(n):
return (
1 if n <= 1 else prod(p ** (e % 3) for p, e in factorint(factorial(n)).items())
)
def A160256_gen(): # generator of terms
yield from [1, 2]
l1, m, b = 2, 1, {1, 2}
while True:
i = m
while True:
if not i in b:
yield i
l1, m = i, l1 // gcd(l1, i)
b.add(i)
break
i += m
def A165562_gen(startvalue=1):
return filter(
lambda n: isprime(n + sum(int(n * e / p) for p, e in factorint(n).items())),
count(max(startvalue, 1)),
)
@lru_cache(maxsize=None)
def A171503(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (A171503(k1) - 1) // 2
j, k1 = j2, n // j2
return 2 * (n * (n - 1) - c + j) - 1
def A175499_gen(): # generator of terms
yield 1
bset, l, s, b = {1}, 2, 3, set()
while True:
i, j = s, s - l
while True:
if not (i in b or j in bset):
yield j
bset.add(j)
b.add(i)
l = i
while s in b:
b.remove(s)
s += 1
break
i += 1
j += 1
def A210503_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
nd = sum(n * e // p for p, e in factorint(n).items())
if is_square(nd**2 + n**2) and gcd(n, nd, isqrt(nd**2 + n**2)) == 1:
yield n
def A235800(n):
return 4 * (n // 2) + 3 if n % 2 else n // 2
def A241816(n):
s = bin(n)[2:]
for i in range(len(s) - 2, -1, -1):
if s[i : i + 2] == "10":
return int(s[:i] + "01" + s[i + 2 :], 2)
else:
return n
def A243103(n):
y, pf = 1, set(primefactors(n))
for m in range(2, n + 1):
if set(primefactors(m)) <= pf:
y *= m
return y
def A257226_gen(startvalue=1):
return filter(
lambda n: any("9" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257225_gen(startvalue=1):
return filter(
lambda n: any("8" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257224_gen(startvalue=1):
return filter(
lambda n: any("7" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257223_gen(startvalue=1):
return filter(
lambda n: any("6" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257222_gen(startvalue=1):
return filter(
lambda n: any("5" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257221_gen(startvalue=1):
return filter(
lambda n: any("4" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257220_gen(startvalue=1):
return filter(
lambda n: any("3" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257219_gen(startvalue=1):
return filter(
lambda n: any("2" in str(d) for d in divisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A257486_gen(): # generator of terms
for l in count(0):
for a in product("34567", repeat=l):
for b in ("4", "5", "6"):
s = "".join(a) + b
if "3" in s and "7" in s:
n = int(s)
if {"3", "7"} <= set(str(n**2)) <= {"3", "4", "5", "6", "7"}:
yield n
def A258981_gen():
return filter(
lambda n: max(gmpy2digits(n, 3)) <= "1",
(int(format(d, "b"), 4) for d in count(0)),
)
def A263132_gen(startvalue=1):
return filter(lambda m: not ~(4 * m - 1) & m, count(max(startvalue, 1)))
def A267769_gen():
return (
int(s, 9)
for s in filter(lambda s: max(s) < "9", (str(i**2) for i in count(0)))
)
def A271472(n):
if n == 0:
return 0
else:
s, q = "", n
while q:
q, r = c_divmod(q, -4)
s += ("0000", "1000", "0011", "1011")[r]
return int(s[::-1])
def A350087(n):
a, b = lucas2(n + 1)
return pow(b, a, a + b)
def A272170_gen(): # generator of terms
a, b = 1, 1
while True:
a, b = b, a + b
yield int(bin(b)[3])
def A272170(n):
return int(bin(fibonacci(n))[3])
def A284597(n):
count, starti, s, i = 0, 1, 0, 1
while True:
d = divisor_count(i)
if d < s:
if count == n:
return starti
starti = i
count = 0
s = d
i += 1
count += 1
def A298684_gen(startvalue=1): # generator of terms
b, a = fib2((sv := max(startvalue, 1)) + 1)
for n in count(sv):
if not (a % (n * (n + 1) * (n + 2) // (1 if n % 2 else 2))):
yield n
a, b = b, a + b
def A306360_gen(startvalue=1): # generator of terms
for k in count(max(startvalue, 1)):
s = str(k)
l, c = len(s), 0
for i in range(l):
c = (c + int(s[i]) ** l) % k
if c == 0:
yield k
def A319651(n):
return int("".join(sorted(gmpy2digits(n, 3), reverse=True)), 3)
def A331761(n):
return (n - 1) ** 2 + 2 * sum(
totient(i) * (n + 1 - 2 * i) * (n + 1 - i) for i in range(2, n // 2 + 1)
)
def A011772(n):
plist = [p**q for p, q in factorint(2 * n).items()]
if len(plist) == 1:
return n - 1 if plist[0] % 2 else 2 * n - 1
return min(
min(crt([m, 2 * n // m], [0, -1])[0], crt([2 * n // m, m], [0, -1])[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
def A344590(n):
m = A011772(n)
return sum(1 for d in divisors(n) if A011772(d) == m)
def A345691(n):
return pvariance(
n**2 * (u**2 + v**2)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A004730(n):
a, b = factorial2(n), factorial2(n + 1)
return a // gcd(a, b)
def A025281(n):
return sum(p * e for p, e in factorint(factorial(n)).items())
def A029732_gen():
return filter(isprime, pal_gen(16))
def A030292_gen(startvalue=0):
return filter(lambda n: len(set(str(n**3))) <= 2, count(max(startvalue, 0)))
def A031749_gen(startvalue=1):
return (
n
for n, d in filter(
lambda x: isinstance(x[1], list) and min(x[1]) == 71,
(
(n, continued_fraction_periodic(0, 1, n)[-1])
for n in count(max(startvalue, 1))
),
)
)
def A038529(n):
return prime(n) - composite(n)
@lru_cache(maxsize=None)
def A046657(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (4 * A046657(k1) - 1)
j, k1 = j2, n // j2
return (n * (n - 1) - c + j) // 4
def A048700(n):
s = bin(n)[2:]
return int(s + s[-2::-1], 2)
def A048890_gen(): # generator of terms
for l in count(1):
for e in "1689":
for d in product("01689", repeat=l):
s = e + "".join(d)
p = int(s)
if p > 0:
q = int(s[::-1].rstrip("0").translate("".maketrans("69", "96")))
if p != q and isprime(q) and isprime(p):
yield p
def A048943_gen(startvalue=1):
return filter(
lambda i: integer_nthroot(i, 4)[1] or not divisor_count(i) % 4,
count(max(startvalue, 1)),
)
def A053782_gen(): # generator of terms
m, s, p = 4, 4, 5
for n in count(1):
if isprime(s):
yield n
m += 1
if m == p:
m += 1
p = nextprime(p)
s += m
def A055472_gen():
return filter(isprime, (n * (n + 1) // 2 + 2 for n in count(0)))
def A059539(n):
return integer_nthroot(3 * n**3, 3)[0]
def A064799(n):
return prime(n) + composite(n)
def A068653_gen(): # generator of terms
for l in count(1):
for m in product(("1379" if l > 1 else "123579"), repeat=l):
for d in "0123456789":
s = "".join(m) + d
n = int(s)
if not isprime(n):
for k in range(len(s) - 1):
s = s[1:] + s[0]
if not isprime(int(s)):
break
else:
yield n
def A074200(n):
a = lcm(range(1, n + 1))
m = a
while True:
for k in range(n, 0, -1):
if not isprime(m // k + 1):
break
else:
return m
m += a
def A074925_gen(startvalue=2):
return filter(
lambda i: prevprime(i**3 // 2) + nextprime(i**3 // 2) == i**3,
count(max(startvalue + startvalue % 2, 2), 2),
)
def A088104(n):
return nextprime((p := prime(n)) * 10 ** (n - len(str(p))) - 1)
def A090693_gen():
return (
i
for i, n in filter(
lambda x: x[0] > 0 and isprime(x[1] + 2),
enumerate(accumulate(range(10**5), lambda x, y: x + 2 * y - 3)),
)
)
def A091938(n):
for i in range(n, -1, -1):
q = 2**n
for d in multiset_permutations("0" * (n - i) + "1" * i):
p = q + int("".join(d), 2)
if isprime(p):
return p
def A099906(n):
return comb(2 * n - 1, n - 1) % (n**2)
def A099908(n):
return comb(2 * n - 1, n - 1) % (n**4)
@lru_cache(maxsize=None)
def A100613(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (k1**2 - A100613(k1))
j, k1 = j2, n // j2
return n + c - j
def A104804_gen(): # generator of terms
blist = [1, 3]
yield from blist
while True:
i, j = isqrt_rem(blist[-1] ** 2 + blist[-2] ** 2)
blist = blist[1:] + [int(i + int(4 * (j - i) >= 1))]
yield blist[-1]
def A105870_gen(): # generator of terms
a, b = 0, 1
while True:
yield a
a, b = b, (a + b) % 7
def A107715_gen():
return filter(isprime, (int(gmpy2digits(n, 4)) for n in count(0)))
def A116017_gen(startvalue=1):
return filter(
lambda n: len(set(str(n + sum(divisors(n))))) == 1, count(max(startvalue, 1))
)
def A121943_gen(): # generator of terms
b = 2
for n in count(1):
if not b % (n**2):
yield n
b = b * (4 * n + 2) // (n + 1)
def A163574_helper(n, b):
if n == 1:
t = list(range(1, b))
for i in range(1, b):
u = list(t)
u.remove(i)
yield i, u
else:
for d, v in A163574_helper(n - 1, b):
for g in v:
k = d * b + g
if not k % n:
u = list(v)
u.remove(g)
yield k, u
def A163574(n):
if n % 2:
return 0
for a, b in A163574_helper(n - 1, n):
return a
return 0
def A168294(n):
s, t = [int(d) for d in str(n)], [int(d) for d in str(n + 1)]
l, m = len(s), len(t)
u = [0] * (l + m - 1)
for i in range(l):
for j in range(m):
u[i + j] = (u[i + j] + s[i] * t[j]) % 10
return int("".join(str(d) for d in u))
def A195527_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
n, c = 3, 0
while n * (n + 1) <= 2 * m:
if not 2 * (n * (n - 2) + m) % (n * (n - 1)):
c += 1
if c > 2:
break
n += 1
if c == 2:
yield m
def A195528_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
n, c = 3, 0
while n * (n + 1) <= 2 * m:
if not 2 * (n * (n - 2) + m) % (n * (n - 1)):
c += 1
if c > 3:
break
n += 1
if c == 3:
yield m
def A196368(n):
return int(all(str(n)[i] != str(n)[i - 1] for i in range(1, len(str(n)))))
def A216822_gen(startvalue=1):
return filter(
lambda n: n == 1 or pow(2, n, n * (n + 1)) == 2, count(max(startvalue, 1))
)
def A226459(n):
return sum(totient(d) * d ** (d - 1) for d in divisors(n, generator=True))
def A241206(n):
for i in range(9, 0, -1):
x = i * (10**n - 1) // 9
for j in range(n - 1, -1, -1):
for k in range(9 - i, -1, -1):
y = x + k * (10**j)
if isprime(y):
return y
for j in range(n):
for k in range(1, i + 1):
if j < n - 1 or k < i:
y = x - k * (10**j)
if isprime(y):
return y
def A247012_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
if not isprime(n):
m = int(str(n)[::-1])
x = divisors(n)
x.pop()
y = divisor_sigma(n) - n
while y < m:
x, y = x[1:] + [y], 2 * y - x[0]
if y == m:
yield n
def A247219_gen(startvalue=2):
return filter(lambda n: pow(2, n, n * n - 1) == 1, count(max(startvalue, 2)))
def A252022_gen(): # generator of terms
l, s, b = [1], 2, set()
yield 1
while True:
i = s
while True:
if i not in b:
li = [int(d) for d in str(i)[::-1]]
for x, y in zip(li, l):
if x + y > 9:
break
else:
l = li
b.add(i)
yield i
while s in b:
b.remove(s)
s += 1
break
i += 1
def A253046(n):
q2, r2 = divmod(n, 2)
if not r2 and isprime(q2):
return 3 * nextprime(q2)
else:
q3, r3 = divmod(n, 3)
if not r3 and isprime(q3):
return 2 * prevprime(q3)
return n
def A259089(n):
s, k2 = "2" * n, 1
for k in count(0):
if s in str(k2):
return k
k2 *= 2
def A267763_gen():
return (
int(d, 3)
for d in filter(lambda d: max(d) < "3", (str(i**2) for i in count(0)))
)
def A269784_gen(): # generator of terms
j = -5
for i in count(0):
if isprime(j):
yield j
j += 4 * (i + 1)
def A286262_gen(startvalue=0):
return filter(lambda n: is_cubefree_string(bin(n)[2:]), count(max(startvalue, 0)))
def A291626_gen(startvalue=1):
return filter(lambda k: min(str(k**2)) == "1", count(max(startvalue, 1)))
def A291630_gen(startvalue=1):
return filter(lambda k: min(str(k**2)) == "5", count(max(startvalue, 1)))
def A291644_gen(startvalue=1):
return filter(lambda k: min(str(k**3)) == "5", count(max(startvalue, 1)))
def A322131(n):
return int("".join(str(int(d) * 2) for d in str(n)))
def A332584(n):
r, m = n, n + 1
while True:
r = r * 10 ** (len(str(m))) + m
if m % 2 == 0 and r % (m + 1) == 0:
return m
m += 1
def A338228(n):
return n - divisor_count(isqrt(n // numbercore(n, 2)))
def A338231(n):
return n * (n + 1) // 2 - divisor_sigma(isqrt(n // numbercore(n, 2)))
def A338233(n):
return 0 if n <= 1 else n - 1 - divisor_count(isqrt(n // numbercore(n, 2)))
def A338234(n):
return (
0 if n <= 1 else n * (n - 1) // 2 - divisor_sigma(isqrt(n // numbercore(n, 2)))
)
def A338236(n):
return isqrt(n) - divisor_count(isqrt(n // numbercore(n, 2)))
def A344993(n):
return 2 * n * (n + 1) + 2 * sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i) for i in range(2, n + 1)
)
def A345428(n):
return sum(
u + v
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A345434(n):
return sum(
u**2 + v**2
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A347306(n):
if n == 1:
return 1
i, j, nset, m = 1, 2, {1}, 2
while True:
k = m
i += 1
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
if k == n:
return i
j = k + 1
nset.add(k)
while m in nset:
m += 1
def A347307_gen(): # generator of terms
yield 1
nset, m, c, j = {1}, 2, 0, 2
while True:
k = m
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
if k > c:
c = k
yield k
j = k + 1
nset.add(k)
while m in nset:
m += 1
def A348004_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
pset = set()
for d in udivisors(n, generator=True):
u = prod(p**e - 1 for p, e in factorint(d).items())
if u in pset:
break
pset.add(u)
else:
yield n
def A001962(n):
return 3 * n + isqrt(5 * n**2)
@lru_cache(maxsize=None)
def A015634(n):
if n == 0:
return 0
c, j = 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A015634(k1)
j, k1 = j2, n // j2
return n * (n + 1) * (n + 2) * (n + 3) // 24 - c + j - n
@lru_cache(maxsize=None)
def A025523(n):
if n == 0:
return 1
c, j = 2, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A025523(k1)
j, k1 = j2, n // j2
return n + c - j
def A051572_gen():
return accumulate(repeat(5), lambda x, _: divisor_sigma(x))
def A057436_gen():
return (int("".join(d)) for l in count(1) for d in product("123456", repeat=l))
def A060984_gen():
return accumulate(repeat(1), lambda x, _: x + isqrt(x) ** 2)
def A066058(n):
if n > 0:
for k in count(0):
m = k
for i in range(n):
s1 = format(m, "b")
s2 = s1[::-1]
if s1 == s2:
break
m += int(s2, 2)
else:
s1 = format(m, "b")
if s1 == s1[::-1]:
return k
else:
return 0
def A066452(n):
return len(
[
x
for x in range(1, n)
if all(
[x % d for d in range(2, n) if (n % d) and (2 * n) % d in [d - 1, 0, 1]]
)
]
)
def A067872(n):
y, x, n2 = n * (n + 2), 2 * n + 3, n**2
m, r = divmod(y, n2)
while r:
y += x
x += 2
m, r = divmod(y, n2)
return m
def A071220_gen(): # generator of terms
for i in count(2):
n = i**3
m = n // 2
if not isprime(m) and prevprime(m) + nextprime(m) == n:
yield primepi(m)
def A071295(n):
return bin(n)[1:].count("0") * bin(n).count("1")
def A078567(n):
return (
(m := isqrt(n - 1)) ** 2 * (1 + m) ** 2 // 4
- m**2 * n
+ sum((n - 1) // i * (2 * n - i * (1 + (n - 1) // i)) for i in range(1, m + 1))
)
def A082806_gen():
return filter(
lambda n: isprime(n) and isprime(sum(int(d) for d in str(n))), pal10_gen()
)
def A085513(n):
return num2words(n).count("e")
def A085831(n):
return (lambda m, r: 2 * sum(r // k for k in range(1, m + 1)) - m * m)(
isqrt(2**n), 2**n
)
def A088754(n):
p = prime(n)
m = n - len(str(p))
return primepi((p + 1) * 10**m) - primepi(p * 10**m)
def A113630(n):
return (
n * (n * (n * (n * (n * (n * (n * (9 * n + 8) + 7) + 6) + 5) + 4) + 3) + 2) + 1
)
def A113963_gen(): # generator of terms
bset, b = {1}, 1
yield b
while True:
a = 1
while a in bset or not (a + b) % (a - b):
a += 1
b = a
yield b
bset.add(b)
def A350034(n):
return n // g if (g := gcd(n, 6)) > 1 else 5 * n + 1
def A350265(n):
return hyperexpand(hyper((-n - 1, 1 - n, -n), (1, 3), -1))
def A115510_gen(): # generator of terms
yield 1
l1, s, b = 1, 2, set()
while True:
i = s
while True:
if i & l1 and not i in b:
yield i
l1 = i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A116018_gen(startvalue=1):
return filter(
lambda n: len(set(str(n + totient(n)))) == 1, count(max(startvalue, 1))
)
def A125289_gen(startvalue=0):
return filter(lambda n: len(set(str(n)) - {"0"}) == 1, count(max(startvalue, 0)))
def A138918_gen():
return (
a
for a, b in filter(
lambda x: not x[1], (divmod(prime(n) + 1, 18) for n in count(1))
)
)
def A161664(n):
return (
lambda m: n * (n + 1) // 2 + m * m - 2 * sum(n // k for k in range(1, m + 1))
)(isqrt(n))
def A161886(n):
return (lambda m: 2 * sum(n // k for k in range(1, m + 1)) + n - 1 - m * m)(
isqrt(n)
)
def A166623_gen(): # generator of terms
for b in count(2):
sublist = []
for l in range(1, b + 2):
for n in combinations_with_replacement(range(b), l):
x = sum(d**d for d in n)
if tuple(sorted(sympydigits(x, b)[1:])) == n:
sublist.append(x)
yield from sorted(sublist)
def A189398(n):
return prod(prime(i) ** int(d) for i, d in enumerate(str(n), start=1))
def A191610_gen():
return chain((0,), accumulate(multiplicity(5, n) for n in count(5, 5)))
def A191871(n):
return 0 if n == 0 else (n // 2 ** multiplicity(2, n)) ** 2
if sys.version_info >= (3, 10):
def A192085(n):
return (n**3).bit_count()
else:
def A192085(n):
return bin(n**3).count("1")
def A192293_gen(startvalue=1):
return filter(
lambda n: 3 * n == sum(antidivisors(sum(antidivisors(n)))),
count(max(startvalue, 1)),
)
def A206578(n):
m = 1
while True:
s = continued_fraction_periodic(0, 1, m)[-1]
if isinstance(s, list) and s.count(1) == n:
return m
m += 1
def A212526(n):
s, q = "", -n
while q >= 4 or q < 0:
q, r = divmod(q, -4)
if r < 0:
q += 1
r += 4
s += str(r)
return int(str(q) + s[::-1])
def A217465_gen(startvalue=1):
return filter(
lambda n: pow(2, n, n * (n + 1)) == 2 and not isprime(n),
count(max(startvalue, 1)),
)
def A219326_gen(startvalue=1):
for n in count(max(startvalue, 1)):
s = [int(d) for d in str(n)][::-1]
m = len(s)
if n == Matrix(m, m, lambda i, j: s[(i - j) % m]).det():
yield n
def A236174(n):
p = prime(n)
for b in range(2, 11):
x, y, z = p, 0, 1
while x >= b:
x, r = divmod(x, b)
y += r * z
z *= 10
y += x * z
if isprime(y):
return y
if sys.version_info >= (3, 10):
def A245788(n):
return n * n.bit_count()
else:
def A245788(n):
return n * bin(n).count("1")
def A246029(n):
return (
prod(prime(len(d)) for d in split("0+", bin(n)[2:]) if d != "") if n > 0 else 1
)
def A246593(n):
s = bin(n)[2:]
s2 = s.rstrip("0")
s3 = s2.lstrip("1")
return (
int(s2[: -len(s3)] + "1" + s3[1:-1] + "0" + s[len(s2) :], 2)
if (len(s3) > 0 and n > 1)
else n
)
def A246824_gen():
return (
a
for a, b in ((n, prime(n) + 1) for n in count(3))
if (
not (isprime(b**2 - 1) and isprime(b**2 + 1))
and (min(factorint(b**2 + 1)) > min(factorint(b**2 - 1)) >= b - 1)
)
)
def A247248(n):
if n == 1:
return 1
else:
x, k, kr = 1, 0, 0
while (x + kr) % n:
x, kr = (2 * x) % n, (kr + 1) % n
k += 1
return k
def A247647_gen():
return (int(bin(n)[2:]) for n in count(1) if n % 2 and not "00" in bin(n))
def A248909(n):
return prod((1 if (p - 1) % 6 else p) ** e for p, e in factorint(n).items())
def A259091(n):
s, k, k2 = str(n) * 2, 0, 1
while True:
if s in str(k2):
return k
k += 1
k2 *= 2
def A259092(n):
s, k, k2 = str(n) * 3, 0, 1
while True:
if s in str(k2):
return k
k += 1
k2 *= 2
def A261018_gen(): # generator of terms
a = 1
for i in count(0):
b, s = 1, format(a, "b")
while format(b, "b") in s:
b += 1
a += b
s = format(a, "b")
yield b
def A264596(n):
return sorted(format(i, "b")[::-1] for i in range(n + 1)).index(
format(n, "b")[::-1]
)
def A267490_gen():
return (
int(s, 8)
for s in (str(i**2) for i in count(0))
if max(s) < "8" and isprime(int(s, 8))
)
def A268412_gen(startvalue=0):
return (
i
for i in count(max(startvalue, 0))
if not len(list(filter(bool, format(i, "b").split("0")))) % 2
)
def A268415_gen(startvalue=0):
return (
i
for i in count(max(startvalue, 0))
if len(list(filter(bool, format(i, "b").split("0")))) % 2
)
def A275256_gen(): # generator of terms
for m in count(2):
n, c = 3, 0
while (n * (n + 1)) <= 2 * m:
if not 2 * (n * (n - 2) + m) % (n * (n - 1)):
c += 1
if c >= 6:
break
n += 1
if c >= 6:
yield m
def A275600_gen():
return (
n
for n in (int(gmpy2digits(m, 3), 6) for m in range(10**6))
if max(gmpy2digits(n, 5)) <= "2" and max(gmpy2digits(n, 4)) <= "2"
)
def A276854(n):
return n + isqrt(5 * n**2)
def A289676(n):
c, k, r, n2, cs, ts = (
0,
1 + (n - 1) // 3,
2 ** ((n - 1) % 3),
2 ** (n - 1),
set(),
set(),
)
for i in range(2**k):
j, l = int(bin(i)[2:], 8) * r, n2
traj = set([(l, j)])
while True:
if j >= l:
j = j * 16 + 13
l *= 2
else:
j *= 4
l //= 2
if l == 0:
c += 1
ts |= traj
break
j %= 2 * l
if (l, j) in traj:
cs |= traj
break
if (l, j) in cs:
break
if (l, j) in ts:
c += 1
break
traj.add((l, j))
return c
def A291625_gen(startvalue=1):
return (k for k in count(max(startvalue, 1)) if "0" in str(k**2))
def A301273_gen(): # generator of terms
mu = Fraction(0)
for i in count(1):
mu += (prime(i) - mu) / i
yield mu.numerator
def A301273(n):
return (p := sum(prime(i) for i in range(1, n + 1))) // gcd(p, n)
def A301274_gen(): # generator of terms
mu = Fraction(0)
for i in count(1):
mu += (prime(i) - mu) / i
yield mu.denominator
def A301274(n):
return n // gcd(n, sum(prime(i) for i in range(1, n + 1)))
def A301275_gen(): # generator of terms
yield 0
mu, variance = Fraction(prime(1)), Fraction(0)
for i in count(2):
datapoint = prime(i)
newmu = mu + (datapoint - mu) / i
variance = (variance * (i - 2) + (datapoint - mu) * (datapoint - newmu)) / (
i - 1
)
mu = newmu
yield variance.numerator
def A301276_gen(): # generator of terms
yield 1
mu, variance = Fraction(prime(1)), Fraction(0)
for i in count(2):
datapoint = prime(i)
newmu = mu + (datapoint - mu) / i
variance = (variance * (i - 2) + (datapoint - mu) * (datapoint - newmu)) / (
i - 1
)
mu = newmu
yield variance.denominator
@lru_cache(maxsize=None)
def A304176_helper(n, i):
return (
1
if n == 0 or i == 1
else A304176_helper(n, i - 1) + A304176_helper(n - i, min(i, n - i))
)
def A304176(n):
return A304176_helper(n**3 - n, n)
def A306612(n):
plist, x = [prime(i) for i in range(1, n + 1)], 3
rlist = [-x % p for p in plist]
while True:
for i in range(n - 1):
if rlist[i] >= rlist[i + 1]:
break
else:
return x
for i in range(n):
rlist[i] = (rlist[i] - 1) % plist[i]
x += 1
def A308190(n):
c, x = 0, n
while x != 5:
y = min(factorint(x))
x = y + x // y
c += 1
return c
def A317058_helper(n, p, q): # compute (-n + sum_{k=1,n} k^p) mod q
c = (-n) % q
for k in range(1, n + 1):
c = (c + pow(k, p, q)) % q
return c
def A317058(n):
k = 2
while isprime(k) or A317058_helper(n, k - 1, k):
k += 1
return k
def A320037(n):
return int(
"".join(
d + "0" if "1" in d else d + "1"
for d in split("(0+)|(1+)", bin(n)[2:])
if d != "" and d != None
),
2,
)
def A320038(n):
return int(
"".join(
"0" + d if "1" in d else "1" + d
for d in split("(0+)|(1+)", bin(n)[2:])
if d != "" and d != None
),
2,
)
def A321005_gen(): # generator of terms
plist = [2]
for n in count(0):
c, p = 0, plist[-1]
for j in range(n):
pj = plist[j]
for i in range(j):
if (plist[i] * pj) % p == 1:
c += 1
yield c
plist.append(nextprime(p))
def A321801(n):
return int(
"0"
+ "".join(
d if len(d) == 1 else ""
for d in split("(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)", str(n))
if d != "" and d != None
)
)
def A321802(n):
return (lambda x: int(x) if x != "" else -1)(
"".join(
d if len(d) == 1 else ""
for d in split("(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)", str(n))
if d != "" and d != None
)
)
def A323832_helper(n):
x = 2 * n
y = A321801(x)
while x != y:
x, y = y, A321801(y)
return x
def A323832(n):
mset, m, c = set(), n, 0
while True:
if m == 1 or m == 0 or m == 5:
return c
m = A323832_helper(m)
if m in mset:
return -1
mset.add(m)
c += 1
def A325148_gen(startvalue=0): # generator of terms
if startvalue == 0:
yield 0
j = isqrt(startvalue)
if j * j < startvalue:
j += 1
for n in count(max(j, 0)):
n2 = n**2
for m in divisors(n2):
if m > n:
break
if m == int(str(n2 // m)[::-1]):
yield n2
break
def A338434(n):
m = integer_nthroot(n, 2)[0]
return m * (m + 1) // 2 - divisor_sigma(
integer_nthroot(n // numbercore(n, 2), 2)[0]
)
def A342068(n):
k, a, b, c = 2, 0, primepi(n), primepi(2 * n)
while a + c <= 2 * b:
k += 1
a, b, c = b, c, primepi(k * n)
return k
def A345422(n):
return igcdex(11, prime(n))[0]
def A345692(n):
zlist = [
z
for z in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if z[2] == 1
]
return pvariance(len(zlist) * u for u, v, w in zlist)
def A346004(n):
return ((n + 1) // 2) ** 2 if n % 2 else n
def A347042(n):
fs = factorint(n, multiple=True)
return sum(
len(list(multiset_combinations(fs, d)))
for d in divisors(len(fs), generator=True)
)
def A347045(n):
fs = factorint(n, multiple=True)
q, r = divmod(len(fs), 2)
return 1 if r else prod(fs[:q])
def A347046(n):
fs = factorint(n, multiple=True)
q, r = divmod(len(fs), 2)
return 1 if r else prod(fs[q:])
def A008849_gen(startvalue=1):
return filter(
lambda n: is_square(
prod((p ** (3 * q + 1) - 1) // (p - 1) for p, q in factorint(n).items())
),
count(max(startvalue, 1)),
)
def A011966_gen(): # generator of terms
yield 1
blist, b = [2, 3, 5], 5
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
yield blist[-4]
def A011969_gen(): # generator of terms
yield from [1, 3]
blist, b, b2 = [1], 1, 1
while True:
blist = list(accumulate([b] + blist))
yield 2 * b + b2 + blist[-1]
b2, b = b, blist[-1]
@lru_cache(maxsize=None)
def A015616(n):
if n <= 1:
return 0
c, j = n * (n - 1) * (n - 2) // 6, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c -= (j2 - j) * A015616(k1)
j, k1 = j2, n // j2
return c
@lru_cache(maxsize=None)
def A015650(n):
if n == 0:
return 0
c, j = n + 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A015650(k1)
j, k1 = j2, n // j2
return n * (n + 1) * (n + 2) * (n + 3) * (n + 4) // 120 - c + j
def A336643(n):
return prod(primefactors(n)) // numbercore(n)
def A336644(n):
return (n - prod(primefactors(n))) // numbercore(n)
def A350390(n):
return n * numbercore(n) // prod(primefactors(n))
def A008833(n):
return n // numbercore(n)
def A016070_gen(startvalue=1):
return filter(
lambda n: len(s := set(str(n**2))) == 2
and s not in [{"0", "1"}, {"0", "4"}, {"0", "9"}],
count(max(startvalue, 1)),
)
def A017714(n):
return comb(n, 50)
def A022519_gen(): # generator of terms
b = 8
while True:
yield b
b = int("".join(str(k) + str(len(list(g))) for k, g in groupby(str(b)[::-1])))
def A025502(n):
m, tlist, s = 10**n, [1, 2], 0
while tlist[-1] + tlist[-2] <= m:
tlist.append(tlist[-1] + tlist[-2])
for d in tlist[::-1]:
if d <= m:
s += 1
m -= d
return s
def A028820_gen():
return chain(
(0,),
(
n
for n in (
int("".join(i))
for l in count(1)
for i in combinations_with_replacement("123456789", l)
)
if is_square(n)
),
)
def A030666(n):
d, nd = 10, 10 * n
while True:
x = (isqrt(nd - 1) + 1) ** 2
if x < nd + d:
return int(x)
d *= 10
nd *= 10
def A046358_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if not isprime(n)
and not n % (m := sum(p * e for p, e in factorint(n).items()))
and str(m) == str(m)[::-1]
)
def A047972(n):
return min((p := prime(n)) - (a := isqrt(p)) ** 2, (a + 1) ** 2 - p)
def A052072(n):
a, b, c = 0, 0, 0
for i in count(0):
s = str(c)
for d in set(s):
if s.count(d) != n:
break
else:
return c
c += a + b + 1
b += 2 * a + 3
a += 3
def A052091_gen(): # generator of terms
yield 2
p = 2
while True:
m, ps = 1, str(p)
s = int("1" + ps + "1")
while not isprime(s):
m += 1
ms = str(m)
if ms[0] in "268":
ms = str(int(ms[0]) + 1) + "0" * (len(ms) - 1)
m = int(ms)
if ms[0] in "45":
ms = "7" + "0" * (len(ms) - 1)
m = int(ms)
s = int(ms + ps + ms[::-1])
p = s
yield m
def A052092_gen(): # generator of terms
yield 1
l, p = 1, 2
while True:
m, ps = 1, str(p)
s = int("1" + ps + "1")
while not isprime(s):
m += 1
ms = str(m)
if ms[0] in "268":
ms = str(int(ms[0]) + 1) + "0" * (len(ms) - 1)
m = int(ms)
if ms[0] in "45":
ms = "7" + "0" * (len(ms) - 1)
m = int(ms)
s = int(ms + ps + ms[::-1])
p = s
l += 2 * len(ms)
yield l
def A063095(n):
c, p = 0, 2
for i in range(n):
q = nextprime(p)
c, p = max(c, q - p), q
return c
def A063527_gen(): # generator of terms
for g in count(1):
for n in product("123456789", repeat=g):
s = "".join(n)
m = int(s)
if not any([m % int(d) for d in s]):
for i in range(len(s) - 1):
if m % int(s[i : i + 2]):
break
else:
yield m
def A067563(n):
return prime(n) * composite(n)
def A068084(n):
u, v, t = 4 * (n + 1), (2 * (n + 1)) ** 2 - 1, 4 * n * (n + 1)
while True:
if not v % t:
return v // 8
v += u + 1
u += 2
def A069706_gen(): # generator of terms
yield from [2, 3, 5, 7]
for i in count(5):
p = prime(i)
s = str(p)
if isprime(int(s[-1] + s[1:-1] + s[0])):
yield p
def A075075_gen(): # generator of terms
yield from [1, 2]
l1, m, b = 2, 2, {1, 2}
while True:
i = m
while True:
if not i in b:
yield i
l1, m = i, i // gcd(l1, i)
b.add(i)
break
i += m
def A080478_gen(): # generator of terms
yield 1
a = 1
while True:
a += 1
b = 2 * a * (a - 1) + 1
while not isprime(b):
b += 4 * (a + 1)
a += 2
yield a
def A091507(n):
return prod(d for d in range(2, n) if n % d and 2 * n % d in [d - 1, 0, 1])
def A094685(n):
i, j = isqrt_rem(n**3 if n % 2 else n)
return int(i + int(4 * (j - i) >= 1))
def A100384(n):
k, a = 2, [max(factorint(m + 2)) for m in range(n)]
while True:
for i in range(1, n):
if a[i - 1] >= a[i]:
break
else:
return k
a = a[i:] + [max(factorint(k + j + n)) for j in range(i)]
k += i
def A104301_gen(): # generator of terms
for n in count(1):
x = int(str((n + 1) ** 2) + str(n**2))
if isprime(x):
yield x
def A110713(n):
return len(
{prod(d) for d in combinations_with_replacement(list(range(1, n + 1)), n)}
)
def A114065_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if sorted(str(divisor_sigma(n))) == sorted(str(totient(n))) == sorted(str(n))
)
def A117345_gen(): # generator of terms
plist = [2, 3, 5, 7, 11, 13, 17, 19, 23]
for k in count(1):
if Matrix(plist).reshape(3, 3).det() == 0:
yield k
plist = plist[1:] + [nextprime(plist[-1])]
def A117960():
return filter(
lambda n: set(str(n)) <= {"1", "3", "5", "7", "9"},
(m * (m + 1) // 2 for m in count(0)),
)
def A119908_gen(): # generator of terms
c, s = {}, 3
for n in count(2):
for p, e in factorint(4 * n - 2).items():
if p in c:
c[p] += e
else:
c[p] = e
for p, e in factorint(n + 1).items():
if c[p] == e:
del c[p]
else:
c[p] -= e
if n == s:
c2 = [p for p, e in c.items() if e >= 2]
yield 1 if c2 == [] else max(c2)
s = 2 * s + 1
def A130334(n):
k, Tn, Tm = n + 1, n * (n + 1) // 2, (n + 1) * (n + 2) // 2
while gcd(Tn, Tm) != 1:
k += 1
Tm += k
return k
@lru_cache(maxsize=None)
def A137243(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (A137243(k1) // 4 - 1)
j, k1 = j2, n // j2
return 4 * (n * (n - 1) - c + j)
def A155150_gen(startvalue=1):
return filter(lambda n: len(set(str(n**4))) == 4, count(max(startvalue, 1)))
def A175795_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if sorted(str(divisor_sigma(n))) == sorted(str(totient(n)))
)
def A178029_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if sum([d for d in range(2, n) if (n % d) and (2 * n) % d in [d - 1, 0, 1]])
== sum(divisors(n))
)
def A185704(n):
p, k, m = 2, 73**n, 10
q, m2 = p % k, m % k
while True:
p = nextprime(p)
while p >= m:
m *= 10
m2 = m % k
q = (q * m2 + p) % k
if q == 0:
return p
def A188187(n):
return isqrt(5 * n**2) - isqrt(5 * (n - 1) ** 2) - 2
def A206585(n):
i = 2
while True:
s = continued_fraction_periodic(0, 1, i)[-1]
if isinstance(s, list) and s.count(5) == n:
return i
i += 1
def A209252(n):
return len(
[
1
for i in range(len(str(n)))
for d in "0123456789"
if d != str(n)[i] and isprime(int(str(n)[:i] + d + str(n)[i + 1 :]))
]
)
def A214560(n):
return bin(n * n)[2:].count("0")
def A214842_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not (
sum([d for d in range(2, n, 2) if n % d and not 2 * n % d])
+ sum([d for d in range(3, n, 2) if n % d and 2 * n % d in [d - 1, 1]])
)
% n
)
def A215199(n):
l = len(str(3**n)) - 1
l10, result = 10**l, 2 * 10**l
while result >= 2 * l10:
l += 1
l102, result = l10, 20 * l10
l10 *= 10
q, qn = 2, 2**n
while qn <= l10:
s, sn = 2, 2**n
while sn <= l10:
if s != q:
a, b = crt([qn, sn], [0, 1])
if a <= l102:
a = b * (l102 // b) + a
while a < l10:
p, t = a // qn, (a - 1) // sn
if p != q and t != s and isprime(p) and isprime(t):
result = min(result, a - 1)
a += b
s = nextprime(s)
sn = s**n
q = nextprime(q)
qn = q**n
return result
def A215659_gen(): # generator of terms
for i in count(1):
a, b = integer_nthroot(4 * primorial(i) + 1, 2)
if b:
yield (a + 1) // 2
def A218013_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not prod(int(d) for d in str(n**2) if d != "0") % n
)
def A228410_gen(): # generator of terms
yield 1
l, s, b = Counter("1"), 2, set()
while True:
i = s
while True:
if i not in b:
li, o = Counter(str(i)), 0
for d in (l + li).values():
if d % 2:
if o > 0:
break
o += 1
else:
yield i
l = li
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A228768(n):
m = 1
while True:
m = nextprime(m)
for b in range(2, n + 1):
if not is_emirp(m, b):
break
else:
return m
def A235807_gen(startvalue=0):
return filter(lambda n: len(set(str(n**3))) == 5, count(max(startvalue, 0)))
def A236437_gen():
return (p for n in count(1) if A236174(n) == (p := prime(n)))
def A240960_gen():
return filter(
lambda x: sum(divisors(x)) - totient(x)
== divisor_count(x) ** len(primefactors(x)),
count(1),
)
def A242788_gen():
return chain((1, 2, 4, 5, 6), (n for n in count(7) if pow(n, n, n - 3) == 3))
def A246198_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
d = divisors(n)
d.remove(n)
s, dmax = sum(d), max(d)
if not s % 2 and 2 * dmax <= s:
d.remove(dmax)
s2 = s / 2 - dmax
for x in range(2 ** len(d)):
if sum(Subset.unrank_binary(x, d).subset) == s2:
yield n
break
def A246591(n):
if n <= 1:
return n
else:
s = bin(n)[2:]
l = len(s)
y = 2**l - 1
for i in combinations(range(l), 2):
s2 = int(
s[: i[0]] + s[i[1]] + s[i[0] + 1 : i[1]] + s[i[0]] + s[i[1] + 1 :], 2
)
if s2 < y:
y = s2
return y
def A246592(n):
s = bin(n)[2:]
for i in range(len(s) - 1):
if s[i : i + 2] == "10":
return int(s[:i] + "01" + s[i + 2 :], 2)
else:
return n
def A246594(n):
s = bin(n)[2:]
for i in range(len(s) - 1):
if s[i : i + 2] == "01":
return int(s[:i] + "10" + s[i + 2 :], 2)
else:
return n
def A246714_gen(): # generator of terms
yield 1
c = 1
for n in count(2):
c = c * (4 * n - 2) // (n + 1)
yield c % prime(n)
def A349949(n):
return sum(
1
for m in filter(
lambda d: not (
((n - 1) % (d - 1) if d > 1 else True)
and (n - 1) % (d + 1)
and ((n + 1) % (d - 1) if d > 1 else True)
and (n + 1) % (d + 1)
),
divisors(n, generator=True),
)
)
def A246830_gen(): # generator of terms
for n in count(0):
for k in range(n):
yield int(bin(n - k)[2:] + bin(n + k)[2:], 2)
yield 2 * n
def A246830_T(n, k):
return int(bin(n - k)[2:] + bin(n + k)[2:], 2)
def A246972(n):
return int(str((n + 1) ** 2) + str(n**2))
def A247013_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
m = int(str(n)[::-1])
if n % 10 and not isprime(n):
x = sorted(chain.from_iterable([p] * e for p, e in factorint(n).items()))
y = sum(x)
while y < m:
x, y = x[1:] + [y], 2 * y - x[0]
if y == m:
yield n
def A247190(n):
p, f, fv = prime(n), 1, {}
for i in range(2, p):
f = (f * i) % p
if f in fv:
return fv[f]
else:
fv[f] = i
else:
return 0
def A247220_gen(startvalue=0):
return (i for i in count(max(startvalue, 0)) if pow(2, i, i * i + 1) == i * i)
def A247358_gen():
return chain.from_iterable(
sorted((b + 1) ** (n - b) for b in range(n)) for n in count(1)
)
def A251240_gen(): # generator of terms
l1, l2, s, b = 3, 2, 4, {}
for n in count(4):
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
l2, l1, b[i] = l1, i, 1
while s in b:
b.pop(s)
s += 1
k, l = integer_nthroot(i, 2)
if l and is_prime(k):
yield n
break
i += 1
def A251555_gen(): # generator of terms
yield from [1, 3, 2]
l1, l2, s, b = 2, 3, 4, set()
while True:
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
yield i
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A253050_gen(): # generator of terms
yield from [0, 1, 0]
l1, l2, s, b = 2, 1, 3, set()
while True:
i = s
while True:
if not (i in b or i & l1) and i & l2:
yield i & 1
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A253412(n):
c, fs = 0, "0" + str(n) + "b"
for i in range(2**n):
s = "01" + format(i, fs) + "10"
for j in range(n):
if (
s[j : j + 4] == "0100"
or s[j + 1 : j + 5] == "0010"
or s[j + 1 : j + 4] == "000"
or s[j + 1 : j + 4] == "111"
):
break
else:
c += 1
return c
def A253574_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if set(str(n)) & set(str(n**4)) == set() and isprime(n)
)
def A253646_gen(startvalue=2): # generator of terms
if startvalue <= 2:
yield 2
for i in count(max(startvalue, 3), 2):
if not "0" in str(i):
m = i
for k in range(5):
m *= i
if "0" in str(m):
break
else:
if isprime(i):
yield i
def A254334_gen():
return (
int("".join(format(x, "02d") for x in sympydigits(3**i, 60)[1:]))
for i in count(0)
)
def A256229(n):
y = 1
for d in reversed(str(n)):
y = int(d) ** y
return y
def A257763_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not "0" in str(n) and set(str(n)) == set(str(n**2))
)
def A257893_gen(startvalue=1): # generator of terms
l = []
for d in permutations("0123456789", 10):
if d[0] != "0":
d2 = int("".join(d))
if d2 >= startvalue:
d = d2
r = d2 % 2
while not r:
d2, r = divmod(d2, 2)
l.append((d2, d))
l.sort()
yield from (b for a, b in l)
def A270807_gen(): # generator of terms
b = 1
while True:
yield b
b += b // (max(primefactors(b) + [1])) + 1
def A271713_gen():
return ((n**2 + 5) // 3 for n in count(0) if not (n**2 + 5) % 3)
def A272653_gen():
return (
int(b + "".join(s), 2)
for b in (bin(n)[2:] for n in count(1))
for s in multiset_permutations(sorted(b))
)
def A272679(n):
if n == 0:
return 0
else:
d, nd = 1, n
while True:
x = isqrt(nd - 1) + 1
if x**2 < nd + d:
return int(x)
d *= 2
nd *= 2
def A276466(n):
return sum(Fraction(d, 10 ** len(str(d))) for d in divisors(n)).numerator
def A279204(n):
return int(str(n) + str(n + 1) + str(n + 2) + str(n + 3))
def A289776(n):
i = 1
while len(divisors(i)) < n or not isprime(sum(divisors(i)[:n])):
i += 1
return i
def A291301(n):
m = primorial(n)
while not isprime(m):
m = divisor_sigma(m) - 1
return m
def A291302(n):
m, c = primorial(n), 0
while not isprime(m):
m = divisor_sigma(m) - 1
c += 1
return c
def A291672_gen(startvalue=1):
return (k for k in count(max(startvalue, 1)) if min(str(k**4)) == "4")
def A298463_gen(): # generator of terms
m = 6
for n in count(1):
k = prevprime(m // 2)
if k + nextprime(k) == m:
yield n * (3 * n - 1) // 2
m += 6 * n - 1
def A298464_gen(): # generator of terms
m = 6
for n in count(1):
k = prevprime(m // 2)
if k + nextprime(k) == m:
yield k
m += 6 * n - 1
def A298465_gen(): # generator of terms
m = 8
for n in count(1):
k = prevprime(m // 2)
if k + nextprime(k) == m:
yield n * (5 * n - 3) // 2
m += 10 * n - 3
def A298466_gen(): # generator of terms
m = 8
for n in count(1):
k = prevprime(m // 2)
if k + nextprime(k) == m:
yield k
n += 1
m += 10 * n - 3
def A303260(n):
return Matrix(n, n, lambda i, j: (j - i - 1) % n + (i == j)).det()
def A306582(n):
plist, rlist, x = [prime(i) for i in range(1, n + 1)], [0] * n, 0
while True:
for i in range(n - 1):
if rlist[i] >= rlist[i + 1]:
break
else:
return x
for i in range(n):
rlist[i] = (rlist[i] + 1) % plist[i]
x += 1
def A316434(n):
pp = primepi(n)
return 1 if n == 1 or n == 2 else A316434(pp) + A316434(n - pp)
def A317357(n):
k = n + 1
while isprime(k) or A317058_helper(n, k - 1, k):
k += 1
return k
def A317358(n):
k = 2
while A317058_helper(n, k - 1, k):
k += 1
return k
def A326806_gen(startvalue=0): # generator of terms
for n in count(max(startvalue, 0)):
sn = str(n)
if sn in str(n * sum(int(d) for d in sn)):
yield n
def A333548_gen(): # generator of terms
bset, y = {0}, 0
for n in count(1):
y -= n
if y <= 0 or y in bset:
y += 2 * n
bset.add(y)
if y == n + 1:
yield y
def A340740(n):
return sum(n % k for k in range(1, n // 2 + 1) if gcd(k, n) == 1)
def A341656(n):
return divisor_count(prime(n) ** 4 - 1)
def A343590_helper(w, dir):
if dir == 1:
for s in w:
for t in range(int(s[-1]) + 1, 10, 2):
yield s + str(t)
else:
for s in w:
for t in range(1 - int(s[-1]) % 2, int(s[-1]), 2):
yield s + str(t)
def A343590_gen(): # generator of terms
for l in count(0):
for d in "123456789":
x = d
for i in range(1, l + 1):
x = A343590_helper(x, (-1) ** i)
yield from (int(p) for p in x if isprime(int(p)))
if l > 0:
y = d
for i in range(1, l + 1):
y = A343590_helper(y, (-1) ** (i + 1))
yield from (int(p) for p in y if isprime(int(p)))
def A343997(n):
fs = factorint(2 * n)
plist = [p ** fs[p] for p in fs]
x = min(
k
for k in (crt(plist, d)[0] for d in product([0, -1], repeat=len(plist)))
if k > 0
)
return x + x % 2
def A345926(n):
fs = dict((primepi(a), b) for (a, b) in factorint(n).items())
return len(
set(sum(d) for d in multiset_combinations(fs, (sum(fs.values()) + 1) // 2))
)
def A346005(n):
return n if n % 3 == 0 else ((n + 2) // 3) ** 3 if n % 3 == 1 else (n + 1) ** 2 // 3
def A346007(n):
i = (5 - n) % 5
return comb(5, i + 1) * ((n + i) // 5) ** (i + 1)
def A346892_gen():
return (
1000 * n + d
for n in count(0)
for d in [38, 462, 538, 962]
if (lambda x: x[0] == x[1] == x[2] != x[3])(str((1000 * n + d) ** 2))
)
def A347043(n):
fs = factorint(n, multiple=True)
l = len(fs)
return prod(fs[: (l + 1) // 2])
def A347044(n):
fs = factorint(n, multiple=True)
l = len(fs)
return prod(fs[l // 2 :])
def A347594_gen(): # generator of terms
b = 1
for n in count(1):
yield b
m = b**2 + n**2
b = (isqrt(m) + 1) ** 2 - m
def A347754_gen(): # generator of terms
a = 1
for n in count(1):
m = a**2 + n**2
k = isqrt(m) + 1
a = k**2 - m
yield k
def A347756_gen(): # generator of terms
yield 1
nset, m, j = {1}, 2, 2
while True:
k = m
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
j = k + 1
nset.add(k)
if k == m:
yield k
while m in nset:
m += 1
def A348063(n):
return sum(
ff(n, n - k) * expand(ff(symbolx, k)).coeff(symbolx**2)
for k in range(2, n + 1)
)
def A348064(n):
return sum(
ff(n, n - k) * expand(ff(symbolx, k)).coeff(symbolx**3)
for k in range(3, n + 1)
)
def A348065(n):
return sum(
ff(n, n - k) * expand(ff(symbolx, k)).coeff(symbolx**4)
for k in range(4, n + 1)
)
def A348068(n):
return sum(
ff(n, n - k) * expand(ff(symbolx, k)).coeff(symbolx**5)
for k in range(5, n + 1)
)
@lru_cache(maxsize=None)
def A003318(n):
if n == 0:
return 1
c, j = n + 1, 1
k1 = (n - 1) // j
while k1 > 1:
j2 = (n - 1) // k1 + 1
c += (j2 - j) * A003318(k1)
j, k1 = j2, (n - 1) // j2
return c - j
def A011970_gen(): # generator of terms
yield from [1, 4, 8]
blist, b, b2, b3 = [1, 2], 2, 1, 1
while True:
blist = list(accumulate([b] + blist))
yield 3 * (b + b2) + b3 + blist[-1]
b3, b2, b = b2, b, blist[-1]
def A011972_gen(): # generator of terms
yield 1
blist = [1]
while True:
b = blist[-1]
blist = list(accumulate([b] + blist))
yield from blist[1:]
def A014237(n):
return 1 if n == 1 else prime(n) - composite(n - 1)
def A017764(n):
return comb(n, 100)
def A017764_gen(): # generator of terms
m = [1] * 101
while True:
yield m[-1]
for i in range(100):
m[i + 1] += m[i]
def A022797(n):
return 3 if n == 1 else prime(n) + composite(n - 1)
def A028819_gen():
return chain(
(0,),
(
int(isqrt(n))
for n in (
int("".join(i))
for l in count(1)
for i in combinations_with_replacement("123456789", l)
)
if is_square(n)
),
)
def A030056_gen(): # generator of terms
b = 1
for n in count(6):
yield b
b = b * (2 * n + 2) * (2 * n + 3) // ((n - 5) * (n + 8))
def A030056(n):
return comb(2 * n + 1, n - 6)
def A030690(n):
d, nd = 10, 10 * n**2
while True:
x = (integer_nthroot(nd - 1, 3)[0] + 1) ** 3
if x < nd + d:
return x
d *= 10
nd *= 10
def A046332_gen():
return (x for x in pal10_gen() if sum(list(factorint(x).values())) == 6)
def A048332_gen():
return chain((0,), (int(d * l, 7) for l in count(1) for d in "123456"))
def A048612(n):
d = divisors((10**n - 1) // 9)
l = len(d)
return (d[l // 2] - d[(l - 1) // 2]) // 2
def A048703(n):
s = bin(n - 1)[2:]
if len(s) % 2:
s = "0" + s
t = [s[i : i + 2] for i in range(0, len(s), 2)]
return int("".join(t + t[::-1]), 2)
def A050804_gen():
return (
2 * i
for i in count(1)
if not any(p % 4 == 1 or factorint(i)[p] % 2 for p in factorint(i))
)
def A055268(n):
return (11 * n + 4) * comb(n + 3, 3) // 4
def A055268_gen(): # generator of terms
m = [11, 1, 1, 1, 1]
while True:
yield m[-1]
for i in range(4):
m[i + 1] += m[i]
def A057045(n):
i, j = isqrt_rem(2 * lucas(n - 1))
return int(i + int(4 * (j - i) >= 1))
def A057332_helper(w, dir):
if dir == 1:
for s in w:
for t in range(int(s[-1]) + 1, 10):
yield s + str(t)
else:
for s in w:
for t in range(0, int(s[-1])):
yield s + str(t)
def A057332(n):
c = 0
for d in "123456789":
x = d
for i in range(1, n + 1):
x = A057332_helper(x, (-1) ** i)
c += sum(1 for p in x if isprime(int(p + p[-2::-1])))
if n > 0:
y = d
for i in range(1, n + 1):
y = A057332_helper(y, (-1) ** (i + 1))
c += sum(1 for p in y if isprime(int(p + p[-2::-1])))
return c
def A057699_gen(): # generator of terms
for l in count(1):
blist = []
for i in range(10 ** (l - 1), 10**l):
if i % 10:
p = int(str(i**3)[::-1])
if isprime(p):
blist.append(p)
yield from sorted(blist)
def A058009(n):
k = n
for _ in range(n):
k = prime(k)
return k
def A060358(n):
return prevprime(lcm(range(1, n + 1)))
def A061906(n):
return A050782(int(str(n).rstrip("0"))) if n > 0 else 1
def A069648(n):
if n == 1:
return 1
else:
m = 2
while True:
x = sum(int(d) for d in str(m**n))
if x > 1 and not any(map(lambda x: x % n, factorint(x).values())):
return m
m += 1
def A071268(n):
s = "".join(str(i) for i in range(1, n + 1))
return (
sum(int(d) for d in s)
* factorial(len(s) - 1)
* (10 ** len(s) - 1)
// (9 * prod(factorial(d) for d in (s.count(w) for w in set(s))))
)
def A070306_gen(startvalue=3): # generator of terms
for i in count(max(startvalue, 3)):
n = i**3
m = n // 3
pm, nm = prevprime(m), nextprime(m)
k = n - pm - nm
if isprime(m):
if m == k:
yield i
else:
if nextprime(nm) == k or prevprime(pm) == k:
yield i
def A076620(n):
return (
y := Poly(prod(symbolx + i for i in range(1, n + 1))).all_coeffs()[::-1]
).index(max(y))
def A078226_gen(): # generator of terms
x = 1
yield 1
while True:
y, x2 = x, 2 * x
while True:
y += x2
s = str(y)
for j in range(len(s) - 1, -1, -2):
if not s[j] in ("1", "3", "5", "7", "9"):
break
else:
for k in range(len(s) - 2, -1, -2):
if not s[k] in ("0", "2", "4", "6", "8"):
break
else:
yield y
x = y
break
def A078227_gen(): # generator of terms
x = 2
yield 2
while True:
y = x
while True:
y += x
s = str(y)
for j in range(len(s) - 1, -1, -2):
if not s[j] in ("0", "2", "4", "6", "8"):
break
else:
for k in range(len(s) - 2, -1, -2):
if not s[k] in ("1", "3", "5", "7", "9"):
break
else:
yield y
x = y
break
def A078242(n):
if n > 0:
for i in range(1, 2**n):
x = 3 * int(bin(i)[2:])
if not x % n:
return x
return 0
def A080719(n):
return int("".join((format(int(d), "b") for d in str(n))), 2)
def A082232_gen():
return filter(
lambda n: not n % sum(int(d) for d in str(n)), islice(pal10_gen(), 1, None)
)
def A087669(n):
c, x = 0, 2 * n + 1
a, b = divmod(x, n)
while b != 0:
x *= a
c += 1
a, b = divmod(x, n)
return c
def A091626(n):
m = isqrt(n)
return 1 if n == 0 else n + sum(n // k for k in range(1, m + 1)) - m * (m - 1) // 2
def A097344_gen(): # generator of terms
yield 1
tlist = [Fraction(1, 1)]
for i in count(1):
for j in range(len(tlist)):
tlist[j] *= Fraction(i, i - j)
tlist += [Fraction(1, (i + 1) ** 2)]
yield sum(tlist).numerator
def A350346_gen(): # generator of terms
yield 0
for n in count(1):
s = bin(n)[2:]
c, l = 0, len(s)
for i in range(l):
c += int(s[l - i - 1])
if 2 * c <= i:
break
else:
yield int(s)
def A036991_gen(startvalue=0): # generator of terms
if startvalue <= 0:
yield 0
for n in count(max(startvalue, 1)):
s = bin(n)[2:]
c, l = 0, len(s)
for i in range(l):
c += int(s[l - i - 1])
if 2 * c <= i:
break
else:
yield n
def A100580_gen():
return filter(isprime, (int(bin(n)[2:]) for n in pal_gen(b=2)))
def A104242_gen():
return filter(isprime, (int(str(n**2) + str((n + 1) ** 2)) for n in count(1)))
def A104265(n):
m, a = integer_nthroot((10**n - 1) // 9, 2)
if not a:
m += 1
k = m**2
while "0" in str(k):
m += 1
k += 2 * m - 1
return k
def A110765(n):
return prod(prime(i) for i, d in enumerate(bin(n)[2:], start=1) if int(d))
def A119861_gen(): # generator of terms
yield 0
c, s = {}, 3
for n in count(2):
for p, e in factorint(4 * n - 2).items():
if p in c:
c[p] += e
else:
c[p] = e
for p, e in factorint(n + 1).items():
if c[p] == e:
del c[p]
else:
c[p] -= e
if n == s:
yield len(c)
s = 2 * s + 1
def A120623_gen(): # generator of terms
b = 1
for n in count(1):
if b % n and not (3 * b) % n:
yield n
b = b * (4 * n + 2) // (n + 2)
def A125094(n):
return (
n
* (
n**2
* (
n**2
* (
n**2
* (n**2 * (n**2 * (n * (210 * n + 1365) + 2730) - 5005) + 8580)
- 9009
)
+ 4550
)
- 691
)
// 2730
)
def A125095(n):
return (
n**2
* (
n**2
* (n**2 * (n**2 * (n**2 * (n * (2 * n + 12) + 22) - 33) + 44) - 33)
+ 10
)
// 24
)
def A123346_gen(): # generator of terms
yield 1
blist = [1]
while True:
b = blist[-1]
blist = list(accumulate([b] + blist))
yield from reversed(blist)
def A130335(n):
k, Tn, Tm = 1, n * (n + 1) // 2, (n + 1) * (n + 2) // 2
while gcd(Tn, Tm) != 1:
k += 1
Tm += k + n
return k
def A133421(n):
return (
n // 2
if not n % 2
else (n // 3 if not n % 3 else (n // 5 if not n % 5 else 7 * n + 1))
)
def A138182(n):
m, tlist = prime(n), [1, 2]
while tlist[-1] + tlist[-2] <= m:
tlist.append(tlist[-1] + tlist[-2])
for d in tlist[::-1]:
if d == m:
return d
elif d < m:
m -= d
def A138290_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
k2, n2 = 1, 2 ** (n + 1)
for k in range(n):
if isprime(n2 - k2 - 1):
break
k2 *= 2
else:
yield n
def A142994(n):
return n * (n * (n * (n * (64 * n + 160) + 240) + 200) + 86) // 15 + 1
def A143010(n):
return (
n
* (
n
* (
n * (n * (n * (n * (n * (35 * n + 140) + 630) + 1400) + 2595) + 3020)
+ 2500
)
+ 1200
)
// 288
+ 1
)
@lru_cache(maxsize=None)
def A143270(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * A143270(k1) // k1 - 1)
j, k1 = j2, n // j2
return n * (n * (n - 1) - c + j) // 2
def A160827(n):
return n * (n * (n * (3 * n + 12) + 30) + 36) + 17
def A169824_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if not n % int(str(n)[::-1]))
def A171865_gen(): # generator of terms
n = 1
for m in A181391_gen():
if m == 0:
yield n
n += 1
def A171868_gen(): # generator of terms
g = A171865_gen()
m = next(g)
for k in g:
yield k - m
m = k
def A171887_gen(): # generator of terms
g = A171868_gen()
n, c = 1, 0
for k in g:
if k > c:
yield n
c = k
n += 1
def A171888_gen(): # generator of terms
g, c = A171868_gen(), 0
for k in g:
if k > c:
yield k
c = k
def A176371_gen():
return filter(
lambda p: is_square(int(str(p)[::-1]) - 13), (prime(n) for n in count(1))
)
def A177719(n):
return 4 * (
(n - 1) * (n - 2)
+ sum(totient(i) * (n - 2 * i) * (n - i) for i in range(2, n // 2 + 1))
)
def A181134(n):
return (
n**2
* (
n**2
* (
n**2
* (
n**2
* (n**2 * (n**2 * (n * (30 * n + 210) + 455) - 1001) + 2145)
- 3003
)
+ 2275
)
- 691
)
// 420
)
def A187338(n):
return 3 * n + isqrt(2 * n**2)
def A187393(n):
return 4 * n + isqrt(8 * n**2)
def A187946(n):
return int(
(isqrt(5 * (n + 5) ** 2) + n + 1) // 2 - (isqrt(5 * n**2) + n) // 2 - 6
)
def A188374(n):
return int(isqrt((n + 2) ** 2 // 2) - isqrt(n**2 // 2)) - 1
def A190402_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if totient(int(sum([n * e / p for p, e in factorint(n).items()]))) == totient(n)
)
def A192290_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if antidivisor_sigma(n) != n and antidivisor_sigma(antidivisor_sigma(n)) == n
)
def A211033(n):
x, y, z = n // 3 + 1, (n - 1) // 3 + 1, (n - 2) // 3 + 1
return (
x**4
+ 4 * x**3 * y
+ 4 * x**3 * z
+ 4 * x**2 * y**2
+ 8 * x**2 * y * z
+ 4 * x**2 * z**2
+ y**4
+ 6 * y**2 * z**2
+ z**4
)
def A211034(n):
x, y, z = n // 3 + 1, (n - 1) // 3 + 1, (n - 2) // 3 + 1
return (
x**2 * y**2
+ 2 * x**2 * y * z
+ x**2 * z**2
+ 2 * x * y**3
+ 6 * x * y**2 * z
+ 6 * x * y * z**2
+ 2 * x * z**3
+ 2 * y**3 * z
+ 2 * y * z**3
)
def A211158(n):
return n * (n + 1) * (3 * n + 1 + 3 * n**2 - (-1) ** n * (2 * n + 1))
def A211349_gen():
return (
p for p in (prime(n) for n in count(1)) if p == 2 or pow(2, p, p - 1) == p - 3
)
def A225671(n):
xn, xd, k, p = 1, prime(n), n, prime(n)
while xn < xd:
k += 1
po, p = p, prime(k)
xn = xn * p + xd
xd *= p
return po
def A228122(n):
k = 0
while sum(factorint(k * (k + 1) + 41).values()) != n:
k += 1
return k
def A229269_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isprime(n - sum(int(n * e / p) for p, e in factorint(n).items()))
)
def A229270_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isprime(sum(int(n * e / p) for p, e in factorint(n).items()) - n)
)
def A229272_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
np = sum(int(n * e / p) for p, e in factorint(n).items())
if isprime(np + n) and isprime(np - n):
yield n
def A229294(n):
ndict = {}
n2 = 2 * n
for i in range(n2):
i3 = pow(i, 2, n2)
for j in range(i + 1):
j3 = pow(j, 2, n2)
m = (i3 + j3) % n2
if m in ndict:
if i == j:
ndict[m] += 1
else:
ndict[m] += 2
else:
if i == j:
ndict[m] = 1
else:
ndict[m] = 2
count = 0
for i in ndict:
j = (n - i) % n2
if j in ndict:
count += ndict[i] * ndict[j]
return count
def A232178(n):
if n == 0:
return 0
t = n * (n + 1) // 2
ds = divisors(t)
l, m = divmod(len(ds), 2)
if m:
return 0
for i in range(l - 1, -1, -1):
x = ds[i]
y = t // x
a, b = divmod(y - x, 2)
if not b:
return a
return -1
def A232179(n):
if n == 0:
return 0
t = 2 * n**2
ds = divisors(t)
for i in range(len(ds) // 2 - 1, -1, -1):
x = ds[i]
y = t // x
a, b = divmod(y - x, 2)
if b:
return a
return -1
def A232444_gen():
return chain(
(2,),
(
n
for n in (d**2 for d in count(1))
if isprime(divisor_sigma(n)) and isprime(divisor_sigma(n**2))
),
)
def A235801_gen(startvalue=0):
return (n if n % 6 != 4 else 10 * (n // 6) + 7 for n in count(max(startvalue, 0)))
def A240923(n):
return (m := Fraction(int(divisor_sigma(n)), n)).numerator - divisor_sigma(
m.denominator
)
def A241557_gen(startvalue=1):
return filter(
lambda n: not any(isprime(d) for d in antidivisors(n, generator=True)),
count(max(startvalue, 1)),
)
def A241107_gen(): # generator of terms
blist = [0, 1, 1, 1, 1, -1]
yield from blist
while True:
blist = blist[1:] + [
(-blist[-1] * blist[-4] + blist[-2] * blist[-3]) // blist[-5]
]
yield blist[-1]
def A242800_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if pow(n, n, n + 3) == n)
def A244411_gen(startvalue=1): # generator of terms
if startvalue <= 1:
yield 1
for n in count(max(startvalue, 2)):
d = divisor_count(n)
if d > 2:
q, r = divmod(d, 2)
s = str(n**q * (isqrt(n) if r else 1))
if s == s[::-1]:
yield n
def A246044_gen(): # generator of terms
for n in count(1):
p = prime(n)
for x in permutations(str(p)):
if x[0] != "0":
p2 = int("".join(x))
if p2 != p and isprime(p2):
break
else:
yield p
def A246519_gen():
return (
p
for p in (prime(n) for n in count(1))
if all(isprime(4 + p**z) for z in (1, 2, 3, 5))
)
def A247165_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if n == 0 or pow(2, n, n * n + 1) == 1)
def A247452_gen(): # generator of terms
yield from [1, 3]
blist, b, n3 = [1], 1, 9
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
yield b * n3
n3 *= 3
def A249153_gen(): # generator of terms
yield 0
n = 0
for i in count(2, 2):
n += multiplicity(2, i) * i
yield n
def A249157_gen():
return filter(lambda n: is_pal(n, 13), pal_gen(11))
def A249158_gen():
return filter(lambda n: is_pal(n, 29), pal_gen(7))
def A249667_gen(): # generator of terms
p = 2
while True:
q = next_prime(p)
n1 = 2 * p + 1
n2 = p + q + 1
while n1 < p + q:
if isprime(n1) and isprime(n2):
yield n1 - p
n1 += 2
n2 += 2
p = q
def A251393_gen(): # generator of terms
yield from [1, 2]
l1, l2, s, p2, b = 3, 2, 4, 4, {}
for n in count(4):
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
l2, l1, b[i] = l1, i, 1
while s in b:
b.pop(s)
s += 1
if i == p2:
yield n
p2 *= 2
break
i += 1
def A251603_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if pow(n, n, n + 2) == 2)
def A252079_gen(): # generator of terms
yield 1
l, s, b = [1], 2, set()
for n in count(2):
i = s
while True:
if i not in b:
li = [int(d) for d in str(i)[::-1]]
for x, y in zip(li, l):
if x + y > 9:
break
else:
l = li
b.add(i)
if i == n:
yield i
while s in b:
b.remove(s)
s += 1
break
i += 1
def A252652(n):
if n == 0:
return 0
f, i, s = 1, 0, re.compile("[0-9]*[1-9]0{" + str(n) + "}[1-9][0-9]*")
while s.match(str(f)) == None:
i += 1
f *= i
return i
def A252865_gen(): # generator of terms
yield from [1, 2, 3]
l1, l2, s, b = 3, 2, 4, set()
while True:
i = s
while True:
if max(factorint(i).values()) == 1:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
yield i
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
else:
b.add(i)
i += 1
def A252868_gen(): # generator of terms
yield from [1, 2, 3]
l1, l2, s, b = 2, 1, 3, set()
while True:
i = s
while True:
if not (i in b or i & l1) and i & l2:
yield A019565(i)
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A253941_gen(): # generator of terms
for p in (prime(n) for n in count(1)):
p2, x = p**2, 1
for i in range(5):
x *= p2
q, r = divmod(x + 5, 6)
if r or not isprime(q):
break
else:
yield p
def A254732(n):
k = n + 1
while pow(k, 2, n):
k += 1
return k
def A254734(n):
k = n + 1
while pow(k, 4, n):
k += 1
return k
def A257345(n):
if n > 0:
for i in range(1, 2**n):
x = int(format(i, "b"))
if not x % n:
return int(str(x), 2)
return 0
def A257349_gen():
return accumulate(repeat(16), lambda x, _: divisor_sigma(x))
def A257899_gen(): # generator of terms
l = []
for d in permutations("0123456789", 10):
if d[0] != "0":
d2 = int("".join(d))
d = d2
r = d2 % 3
while not r:
d2, r = divmod(d2, 3)
l.append((d2, d))
l.sort()
yield from (b for a, b in l)
def A259831_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
s = format(n, "0b")
for l in range(1, len(s)):
n1, n2 = int(s[:l], 2), int(s[l:], 2)
if n2 > 0 and n == (divisor_sigma(n1) - n1) * (divisor_sigma(n2) - n2):
yield n
break
def A259832_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
s, k = format(n, "0b"), divisor_sigma(n)
for l in range(1, len(s)):
n1, n2 = int(s[:l], 2), int(s[l:], 2)
if n2 > 0 and k == (divisor_sigma(n1) - n1) * (divisor_sigma(n2) - n2):
yield n
break
def A262091_gen(): # generator of terms
for m in count(2):
for c in combinations_with_replacement(range(10), m + 1):
n = sum(d**m for d in c)
r = sum(int(q) ** m for q in str(n))
rlist = sorted(int(d) for d in str(r))
rlist = [0] * (m + 1 - len(rlist)) + rlist
if n < r and rlist == list(c):
yield n
def A262092_gen(): # generator of terms
for m in count(2):
for c in combinations_with_replacement(range(10), m + 1):
n = sum(d**m for d in c)
r = sum(int(q) ** m for q in str(n))
rlist = sorted(int(d) for d in str(r))
rlist = [0] * (m + 1 - len(rlist)) + rlist
if n < r and rlist == list(c):
yield r
def A262958_helper1(n):
s = gmpy2digits(n, 3)
m = len(s)
for i in range(m):
if s[i] == "0":
return int(s[:i] + "1" * (m - i), 3)
return n
def A262958_helper2(n):
s = gmpy2digits(n, 4)
m = len(s)
for i in range(m):
if s[i] == "0":
return int(s[:i] + "1" * (m - i), 4)
if s[i] == "2":
return int(s[:i] + "3" + "1" * (m - i - 1), 4)
return n
def A262958_gen(): # generator of terms
n = 1
while True:
m = A262958_helper2(A262958_helper1(n))
while m != n:
n, m = m, A262958_helper2(A262958_helper1(m))
yield m
n += 1
def A263314_gen(startvalue=0): # generator of terms
for i in count(max(startvalue, 0)):
s = str(i)
for d in s:
j = int(d)
if j:
for e in s:
if int(e) % j:
break
else:
yield i
break
def A263856(n):
return 1 + sorted(format(prime(i), "b")[::-1] for i in range(1, n + 1)).index(
format(prime(n), "b")[::-1]
)
def A267821_gen():
return (
int(d, 9)
for d in (str(i**2) for i in count(1))
if max(d) < "9" and isprime(int(d, 9))
)
def A267875(n):
return int((mpz(2) ** 74207281 - 1) // mpz(10) ** (44677235 - n) % 10)
def A268476_gen():
return (
p
for p in (prime(i) for i in count(1))
if not len(list(filter(bool, format(p, "b").split("0")))) % 2
)
def A268477_gen():
return (
p
for p in (prime(i) for i in count(1))
if len(list(filter(bool, format(p, "b").split("0")))) % 2
)
def A271497(n):
return (
int("".join(sorted(bin(n)[2:])), 2)
+ int("".join(sorted(bin(n)[2:], reverse=True)), 2)
if n % 3
else n // 3
)
def A271591_gen(): # generator of terms
a, b, c = 0, 1, 1
while True:
a, b, c = b, c, a + b + c
yield int(bin(c)[3])
def A272363(n):
return (
1
if n == 0
else sum(
1
for p in multiset_partitions(list(range(1, 2 * n + 1)), n)
if max(len(d) for d in p) == 2
and len(set([sum(d) for d in p])) + len(set([abs(d[0] - d[1]) for d in p]))
== 2 * n
)
)
def A272654_gen():
return (
int(b + "".join(s))
for b in (bin(n)[2:] for n in count(1))
for s in multiset_permutations(sorted(b))
)
def A272655_gen():
return (
int(str(n) + "".join(s))
for n in count(1)
for s in multiset_permutations(sorted(str(n)))
)
def A273245_gen():
(
int(m)
for m in (bin(n)[2:] for n in count(1))
if m != m[::-1] and m.rstrip("0") == m[::-1].lstrip("0")
)
def A275111(n):
p, q = prime(n), prime(n + 1)
a = q - 1
for i in range(p + 1, q):
a = (a * igcdex(i, q)[0]) % q
return a
def A276863(n):
return 1 + isqrt(5 * n**2) - isqrt(5 * (n - 1) ** 2)
def A278585_gen():
return (
4 * q - 4
for q in (prime(i) for i in count(1))
if isprime(4 * q - 3)
and isprime(2 * q - 1)
and (not (4 * q - 1) % 3)
and isprime((4 * q - 1) // 3)
)
def A280934_gen(): # generator of terms
yield from [1, 1, 4, 36]
b = 36
for i in count(4):
b += 4 * divisor_count(i + 1) + 8
yield b
@lru_cache(maxsize=None)
def A283207(n):
return 2 if n <= 2 else A283207(n // A283207(n - 1)) + A283207(n // A283207(n - 2))
def A290323(n):
f = factorint(n)
m = f[2] if 2 in f else 0
a, b = divmod(m, 3)
c = 2 if m == 1 else 3 ** (b * (b + 1) % 5) * 5 ** (a - (b % 2))
return c * prod(((d + 1) // 2) ** f[d] for d in f if d != 2)
def A290434_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if sum(factorint(n).values()) == 2
and isprime(1 + sum(factorint(n).keys()) * (3 - len(factorint(n))))
)
def A298946(n):
c = composite(n)
return comb(2 * c - 1, c - 1) % c**4
def A301278(n):
return (
(Fraction(int(comb(2 * n, n))) / n - Fraction(4**n) / (n * (n + 1))).numerator
if n > 0
else 0
)
def A301279(n):
return (
(
Fraction(int(comb(2 * n, n))) / n - Fraction(4**n) / (n * (n + 1))
).denominator
if n > 0
else 1
)
def A301336(n):
return sum(2 * bin(i).count("1") - len(bin(i)) + 2 for i in range(n + 1))
def A306305(n):
m, k = 0, n
while True:
s = str(k)
for i in range(1, len(s)):
if s[i] == s[i - 1]:
return m
m += 1
k *= 2
@lru_cache(maxsize=None)
def A309288(n):
if n <= 1:
return n
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += ((j2 - j) % 2) * (1 - 2 * (j % 2)) * A309288(k1)
j, k1 = j2, n // j2
return c + ((n + 1 - j) % 2) * (1 - 2 * (j % 2))
def A318935(n):
s = bin(n)
return (8 ** (len(s) - len(s.rstrip("0")) + 1) - 1) // 7
def A320039(n):
return int(
"".join(
d + "1" for d in split("(0+)|(1+)", bin(n)[2:]) if d != "" and d != None
),
2,
)
def A320940(n):
return sum(
divisor_sigma(d) * (n // d) ** (n + 1) for d in divisors(n, generator=True)
)
def A321440(n):
if n == 0:
return 1
c = 0
for i in range(n):
mi = i * (i + 1) // 2 + n
for j in range(i + 1, n + 1):
k = mi - j * (j + 1) // 2
if k < 0:
break
if not k % j:
c += 1
return c
def A321797(n):
return int("0" + "".join(d if str(n).count(d) != 1 else "" for d in str(n)))
def A321800(n):
return (lambda x: int(x) if x != "" else -1)(
"".join(d if str(n).count(d) != 1 else "" for d in str(n))
)
def A322781_gen(): # generator of terms
for k in count(1):
fk, fv = zip(*list(factorint(4 * k + 1).items()))
if (
sum(fv) == len(fk) == 2
and fk[0] % 4 == fk[1] % 4 == 1
and legendre_symbol(fk[0], fk[1]) == -1
):
yield 4 * k + 1
def A323271_gen(): # generator of terms
for k in count(1):
fk, fv = zip(*list(factorint(4 * k + 1).items()))
if (
sum(fv) == len(fk) == 3
and fk[0] % 4 == fk[1] % 4 == fk[2] % 4 == 1
and legendre_symbol(fk[0], fk[1])
== legendre_symbol(fk[0], fk[2])
== legendre_symbol(fk[1], fk[2])
== -1
):
yield 4 * k + 1
def A325231_gen(startvalue=6):
return (
n
for n in count(max(startvalue, 6))
if ((not n % 2) and isprime(n // 2))
or (bin(n)[2:4] == "11" and bin(n).count("1") == 2)
)
def A325459(n):
return (
0
if n == 0
else (
lambda m: 2 * (sum(n // k for k in range(1, m + 1)) - n) + (1 - m) * (1 + m)
)(isqrt(n))
)
def A331771(n):
return 4 * (
(n - 1) * (2 * n - 1)
+ sum(totient(i) * (n - i) * (2 * n - i) for i in range(2, n))
)
def A332596(n):
return (
0
if n == 1
else (
(n - 1) * (n - 4)
- sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - 7 * i)
for i in range(2, n // 2 + 1)
)
+ sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i)
for i in range(n // 2 + 1, n + 1)
)
)
// 2
)
def A332867(n):
m, k = int("".join(str(d) for d in range(1, n + 1))), 1
i = n + k
i2, l = i % m, len(str(i))
t = 10**l
t2, r = t % m, i % m
while r != 0:
k += 1
i += 1
i2 = (i2 + 1) % m
if i >= t:
l += 1
t *= 10
t2 = (10 * t2) % m
r = (r * t2 + i2) % m
return k
def A341701(n):
k, m = n, n - 1
while not isprime(k) and m > 0:
k = int(str(k) + str(m))
m -= 1
return m + 1 if isprime(k) else -1
def A341702(n):
k, m = n, n - 1
while not isprime(k) and m > 0:
k = int(str(k) + str(m))
m -= 1
return n - m - 1 if isprime(k) else -1
def A342410(n):
if n == 0:
return 0
for i, d in enumerate(bin(n)[2:].split("0")[::-1]):
if d != "":
return int(d + "0" * i, 2)
def A343996(n):
fs = factorint(2 * n)
plist = [p ** fs[p] for p in fs]
x = min(
k
for k in (crt(plist, d)[0] for d in product([0, -1], repeat=len(plist)))
if k > 0
)
return x + 1 - x % 2
def A345427(n):
return sum(
v
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A345433(n):
return sum(
abs(v)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A345694(n):
zlist = [
z
for z in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if z[2] == 1
]
return pvariance(len(zlist) * abs(u) for u, v, w in zlist)
def A345882_helper(n):
if n == 1:
return {1}
else:
s = A345882_helper(n - 1)
c = set(s)
for x in s:
for i in range(2, n + 1):
c.add(i * x)
return c
def A345882(n):
return len(A345882_helper(n))
def A346006(n):
i = (4 - n) % 4
return comb(4, i + 1) * ((n + i) // 4) ** (i + 1)
def A347323(n):
return int("".join("0" if d == "0" else str(n % int(d)) for d in str(n)))
def A347409(n):
m, r = n, 0
while m > 1:
if m % 2:
m = 3 * m + 1
else:
s = bin(m)[2:]
c = len(s) - len(s.rstrip("0"))
m //= 2**c
r = max(r, c)
return r
def A347607(n):
return partition(n**n)
def A007356_gen(startvalue=0):
return (k for k in count(max(startvalue, 0)) if "666" in str(2**k))
def A008349(n):
return (
n
* (
n
* (n * (n * (n * (n * (n * (57 * n + 108) + 210) + 504) + 273) + 252) + 300)
- 24
)
// 7
+ 1
)
def A011967_gen():
yield 4
blist, b = [5, 7, 10, 15], 15
while True:
blist = list(accumulate([b] + blist))
b = blist[-1]
yield blist[-5]
def A018142(n):
i, j = iroot_rem(10**n, 5)
return int(i) + int(32 * j >= 10 * i * (4 * i * (2 * i * (i + 1) + 1) + 1) + 1)
def A023969(n):
i, j = isqrt_rem(n)
return int(4 * (j - i) >= 1)
def A027603(n):
return n * (n * (4 * n + 18) + 42) + 36
def A036994_gen(startvalue=0): # generator of terms
for n in count(max(startvalue, 0)):
s = bin(n)[2:]
c, l = 0, len(s)
for i in range(l):
c += int(s[l - i - 1])
if 2 * c <= i + 1:
break
else:
yield n
def A028337_gen():
return filter(is_pal, (n * (n + 1) for n in count(1)))
def A028553_gen():
return filter(lambda n: is_pal(n * (n + 3)), count(0))
def A028554_gen():
return filter(is_pal, (n * (n + 3) for n in count(0)))
def A030668(n):
d, nd = 10, 10 * n
while True:
x = (integer_nthroot(nd - 1, 3)[0] + 1) ** 3
if x < nd + d:
return x
d *= 10
nd *= 10
def A031688_gen():
(
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and len(s) % 2 and s[(len(s) - 1) // 2] == 100
)
def A038129(n):
return integer_nthroot(2 * n**3, 3)[0]
def A038585(n):
return int(bin(n)[2:].replace("0", ""))
def A048340_gen():
return chain(
(0,), (int(d * l, 16) for l in range(1, 10) for d in "123456789abcdef")
)
def A048343(n):
y, plist = 0, []
for i in range(10 ** (n - 1), 10**n):
s1 = str(i)
s2 = s1[::-1]
if s1 != s2:
p = i * int(s2)
if not p in plist:
sp = str(p)
if sp == sp[::-1]:
plist.append(p)
y += 1
return y
def A048344_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = str(n)
s2 = str(n)[::-1]
if s != s2:
s3 = str(n * int(s2))
if s3 == s3[::-1]:
yield n
def A048611(n):
d = divisors((10**n - 1) // 9)
l = len(d)
return (d[l // 2] + d[(l - 1) // 2]) // 2
def A051256(n):
return sum(0 if ~n & k else factorial(k + 1) for k in range(n + 1))
def A053095(n):
return sum(
1
for d in multiset_permutations("".join(str(prime(m + 1)) for m in range(n)))
if isprime(int("".join(d)))
)
def A053872_gen(): # generator of terms
m, s = 4, 4
for n in count(1):
if isprime(s):
yield s
m += 1
if isprime(m):
m += 1
s += m
def A056582_gen(): # generator of terms
n = 1
for i in range(2, 201):
m = i**i
yield gcd(n, m)
n *= m
def A057333_helper(w, dir):
if dir == 1:
for s in w:
for t in range(int(s[-1]) + 1, 10):
yield s + str(t)
else:
for s in w:
for t in range(0, int(s[-1])):
yield s + str(t)
def A057333(n):
c = 0
for d in "123456789":
x = d
for i in range(1, n):
x = A057333_helper(x, (-1) ** i)
c += sum(1 for p in x if isprime(int(p)))
if n > 1:
y = d
for i in range(1, n):
y = A057333_helper(y, (-1) ** (i + 1))
c += sum(1 for p in y if isprime(int(p)))
return c
def A057630_gen(startvalue=2): # generator of terms
dlist, p = tuple(str(d) * d for d in range(10)), max(nextprime(startvalue - 1), 2)
while True:
if isprime(int("".join(dlist[int(d)] for d in str(p)))):
yield p
p = nextprime(p)
def A058993_gen(): # generator of terms
m = 5
for k in count(1):
if isprime(int(str(m)[::-1])):
yield k
m *= 5
def A059247(n):
return n // gcd(
n, (lambda m: 2 * sum(n // k for k in range(1, m + 1)) - m * m)(isqrt(n))
)
def A062067_gen(): # generator of terms
yield 1
a = 1
while True:
a += 1
b = 2 * a * (a - 1) + 1
while not isprime(b):
b += 4 * (a + 1)
a += 2
yield a**2
def A062550(n):
return (lambda m: 2 * sum(2 * n // k for k in range(1, m + 1)) - m * m)(
isqrt(2 * n)
)
def A064940_gen(): # generator of terms
p, d, n, r = 2, -1, 0, False
while True:
pn, k = p - n, d if r else -d
if 0 < k <= pn:
yield n + k - 1
d += -pn if r else pn
r, n, p = not r, p, nextprime(p)
def A068186(n):
if n == 1:
return 1
pf = factorint(n)
ps = sorted(pf.keys(), reverse=True)
if ps[0] > 7:
return 0
s = ""
for p in ps:
s += str(p) * (n * pf[p])
return int(s)
@lru_cache(maxsize=None)
def A064960(n):
return (
1 if n == 1 else composite(A064960(n - 1)) if n % 2 else prime(A064960(n - 1))
)
def A068831_gen():
return (
p
for p in (
int("".join(d)) for l in range(1, 9) for d in product("13579", repeat=l)
)
if isprime(p)
and set(str(nextprime(p, 1))) <= {"1", "3", "5", "7", "9"}
and set(str(nextprime(p, 2))) <= {"1", "3", "5", "7", "9"}
and set(str(nextprime(p, 3))) <= {"1", "3", "5", "7", "9"}
)
def A073633_gen(): # generator of terms
m = 1
for n in count(1):
m *= 3
if m // 2**n % n == 0:
yield n
def A073799(n):
return 2 if n == 1 else prime(2**n)
def A073956_gen():
return filter(
lambda n: is_pal(sum(antidivisors(n, generator=True))),
islice(pal10_gen(), 1, None),
)
def A074100_gen():
return (n**3 for n in count(1) if set(str(n**3)) <= set("12357"))
def A075904_gen(startvalue=0):
return filter(lambda k: str(k) in str(k**4), count(max(startvalue, 0)))
def A075905_gen(startvalue=0):
return filter(lambda k: str(k) in str(k**5), count(max(startvalue, 0)))
def A078431(n):
return sum(
1
for p in permutations(range(1, n + 1))
if (lambda x: isprime(x.p) and isprime(x.q))(continued_fraction_reduce(p))
)
def A078432(n):
return sum(
1
for p in permutations(range(1, n + 1))
if isprime(continued_fraction_reduce(p).q)
)
def A078433(n):
return sum(
1
for p in permutations(range(1, n + 1))
if isprime(continued_fraction_reduce(p).p)
)
def A079475(n):
s = str(n)
l = len(s)
if l % 2:
s = s[:-1] + "1" + s[-1]
return int("".join(s[i + 1] * int(s[i]) for i in range(0, l, 2)))
def A080343(n):
i, j = isqrt_rem(2 * n)
return int(4 * (j - i) >= 1)
def A082060_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if set(str(totient(n))) == set(str(n)))
def A082916_gen(): # generator of terms
b = 1
for n in count(0):
if gcd(n, b) == 1:
yield n
b = b * (4 * n + 2) // (n + 1)
def A085300(n):
p = prime(n)
q = p
while True:
m = int(str(q)[::-1])
if isprime(m):
return m
q *= p
def A349823(n):
return (lambda f: sum(f[p] for p in f) * sum(p * f[p] for p in f))(factorint(n))
@lru_cache(maxsize=None)
def A091369(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * A091369(k1) - (k1 * (k1 - 1) + 1))
j, k1 = j2, n // j2
return n * (n - 1) - (c - j) // 2
@lru_cache(maxsize=None)
def A092149(n):
if n == 1:
return 1
c, j = n + 1, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A092149(k1)
j, k1 = j2, n // j2
return j - c
def A096485(n):
return len(continued_fraction(sqrt((10**n - 1) // 9))[-1])
def A096687(n):
if n > 0:
for i in range(1, 2**n):
q, r = divmod(8 * int(bin(i)[2:]), n)
if not r:
return q
return 1
def A105093_gen():
plist = [2, 3, 5, 7]
while True:
m = plist[0] + plist[3]
if m == plist[1] + plist[2]:
yield m
plist = plist[1:] + [nextprime(plist[-1])]
def A113496(n):
m = composite(n)
k = m + 1
while gcd(k, m) != 1 or isprime(k):
k += 1
return k
def A120389(n):
compositepi(prime(n) ** 2)
def A055874(n):
for m in count(1):
if n % m:
return m - 1
def A120624_gen():
b = 1
for n in count(1):
if not b % (2 * n):
yield n
b = b * (4 * n + 2) // (n + 2)
def A127118(n):
return 2 if n == 1 else prime(n) * composite(n - 1)
def A128438(n):
return harmonic(n).q // n
def A130232_gen(): # generator of terms
b, c = 0, 1
while True:
yield b
b += c
c += str(b).count("0")
def A344104_gen(): # generator of terms
b, c = 10, 1
while True:
yield b
b *= c
c += str(b).count("0")
def A138173(n):
d, nd = 1, n**2
while True:
x = integer_nthroot(nd - 1, 3)[0] + 1
if x**3 < nd + d:
return x
d *= 10
nd *= 10
def A147771(n):
i, j = isqrt_rem(n**n)
return int(i + int(4 * (j - i) >= 1))
def A151413(n):
if n <= 2:
return n
else:
l1, m, b = 2, 1, {1, 2}
for j in count(3):
i = m
while True:
if not i in b:
if i == n:
return j
l1, m = i, l1 // gcd(l1, i)
b.add(i)
break
i += m
def A153823(n):
return divisor_count(factorial(n)) - 1
def A155011_gen(): # generator of terms
a, b, a2, b2 = 0, 1, 1, 3
while True:
if isprime(b) and isprime(b2):
yield b
a, b, a2, b2 = b, a + b, b2, a2 + b2 - 1
def A158796_gen(): # generator of terms
for i in count(3):
n = i**3
m = n // 3
pm, nm = prevprime(m), nextprime(m)
k = n - pm - nm
if isprime(m):
if m == k:
yield primepi(pm)
else:
if nextprime(nm) == k:
yield primepi(pm)
elif prevprime(pm) == k:
yield primepi(pm) - 1
def A161501(n):
s = bin(n)[2:]
if s == s[::-1]:
return n
for i in range(1, len(s)):
if s[i:] == s[-1 : i - 1 : -1]:
return int(s + s[i - 1 :: -1], 2)
def A166923(n):
return 1 + (prime(n) ** 2 - 1) % 9
def A167508(n):
return len(set(re.sub("[^a-z]", "", unidecode(num2words(n, lang="fr")))))
def A173071_gen(): # generator of terms
for l in count(1):
for i in combinations("23456789", l):
s = "1" + "".join(i)
p = int(s + s[l - 1 :: -1])
if is_prime(p):
yield p
def A182577(n):
m, tlist, s = factorial(n), [1, 2], 0
while tlist[-1] + tlist[-2] <= m:
tlist.append(tlist[-1] + tlist[-2])
for d in tlist[::-1]:
if d <= m:
s += 1
m -= d
return s
def A185635_gen(): # generator of terms
yield from [1, 2]
l1, m, b = 2, 2, {1, 2}
for n in count(3):
i = m
while True:
if not i in b:
if n == i:
yield i
l1, m = i, i // gcd(l1, i)
b.add(i)
break
i += m
@lru_cache(maxsize=None)
def A185670(n): # based on second formula in A018805
if n == 0:
return 0
c, j = 2, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (k1 * (k1 - 1) + 1 - 2 * A185670(k1))
j, k1 = j2, n // j2
return (c - j) // 2
def A187395(n):
return 4 * n + isqrt(10 * n**2)
def A187396(n):
return isqrt(10 * n**2) - 2 * n
def A188090(n):
return int(isqrt(3 * (n + 5) ** 2) - isqrt(3 * n**2)) - 8
def A188221(n):
return isqrt(5 * (n + 1) ** 2) - isqrt(5 * n**2) - 2
def A188383_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isqrt((n + 3) ** 2 // 2) - isqrt(n**2 // 2) == 3
)
def A191647_gen(startvalue=3):
return (
n
for n in count(max(startvalue, 3))
if isprime(
int(
"".join(
[
str(d)
for d in range(2, n)
if n % d and 2 * n % d in [d - 1, 0, 1]
]
)
)
)
)
def A350457(n):
return (
1
if n == 0
else max(
prod(1 + symbolx ** prime(i) for i in range(1, n + 1)).as_poly().coeffs()
)
)
def A193890_gen(): # generator of terms
for l in count(1):
for d in product("0123", repeat=l):
p = int("".join(d))
if d[0] != "0" and d[-1] in ("1", "3") and isprime(p):
for i in range(len(d)):
d2 = list(d)
d2[i] = str(3 * int(d[i]))
if not is_prime(int("".join(d2))):
break
else:
yield p
def A194145(n):
return isqrt(6 * n**2) - n
def A210205_gen(): # generator of terms
for i in count(3):
n = i**3
p2 = prevprime(n // 3)
p1, p3 = prevprime(p2), nextprime(p2)
q = p1 + p2 + p3
while q <= n:
if q == n:
yield p1
p1, p2, p3 = p2, p3, nextprime(p3)
q = p1 + p2 + p3
def A210546_gen(): # generator of terms
for l in count(1):
q = (10**l - 1) // 9
for i in range(l):
for p in [2, 3, 5, 7]:
r = q + (p - 1) * 10**i
s, t = str(r), str(r)[::-1]
if s != t and isprime(r) and isprime(int(t)):
yield r
def A211203_gen():
return (
p
for p in (prime(n) for n in count(1))
if p == 2 or p == 3 or pow(2, 2 * p - 1, p - 1) == 2
)
def A211889(n):
if n == 1:
return 1
delta = primorial(primepi(n))
p, d = prime(n), delta
while True:
q = p
for _ in range(n):
q += d
if not isprime(q):
break
else:
return d
d += delta
def A212875_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
if not isprime(n):
x = sorted(chain.from_iterable([p] * e for p, e in factorint(n).items()))
y = sum(x)
while y < n:
x, y = x[1:] + [y], 2 * y - x[0]
if y == n:
yield n
def A216384_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
ndsum = nd = sum(int(n * e / p) for p, e in factorint(n).items())
while ndsum <= n and nd > 1:
nd = sum(int(nd * e / p) for p, e in factorint(nd).items())
ndsum += nd
if ndsum == n:
yield n
def A217165(n):
if n == 1:
return 0
else:
l, y, x = tuple(str(d) * n for d in range(10)), 0, 1
for m in count(1):
s = str(x)
for k in l:
if k in s:
return m
y, x = x, y + x
def A217166(n):
if n == 1:
return 0
else:
l, y, x = tuple(str(d) * n for d in range(10)), 2, 1
for m in count(1):
s = str(x)
for k in l:
if k in s:
return m
y, x = x, y + x
def A217466_gen():
return (p for p in (prime(n) for n in count(1)) if pow(2, p, p * (p + 1)) == 2)
def A227510_gen():
return (
int(n)
for n in (str(x) for x in count(1))
if not n.count("0") and str(prod(int(d) for d in n)) in n
)
def A232111(n):
return min(
x
for x in (
sum(d[i] * Fraction(1, i + 1) for i in range(n))
for d in product((1, -1), repeat=n)
)
if x >= 0
).numerator
def A232112(n):
if n <= 1:
return 1
m = lcm(*range(2, n + 1))
mtuple = tuple(m // i for i in range(2, n + 1))
return m // gcd(
m,
min(
abs(m + sum(d[i] * mtuple[i] for i in range(n - 1)))
for d in product((-1, 1), repeat=n - 1)
),
)
def A232175(n):
n3 = n**3
ds = divisors(n3)
for i in range(len(ds) // 2 - 1, -1, -1):
x = ds[i]
y = n3 // x
a, b = divmod(y - x, 2)
if not b:
return a
return 0
def A235540_gen(startvalue=1): # generator of terms
for i in count(max(startvalue, 1)):
if not is_prime(i):
d = 2 * i * (2 * i + 1)
n = (pow(4, i, d) - pow(2, i, d) + 8 * i * i - 2) % d
if not n:
yield i
def A235808_gen(startvalue=0):
return filter(lambda n: len(set(str(n**3))) == 6, count(max(startvalue, 0)))
def A235810_gen(startvalue=0):
return filter(lambda n: len(set(str(n**3))) == 8, count(max(startvalue, 0)))
def A236246_gen(): # generator of terms
n = 1
for m in A229037_gen():
if m == 1:
yield n
n += 1
def A239103_gen(): # generator of terms
for n in count(0):
for k in range(n, -1, -1):
c, d0 = 0, ["0"] * (n + k)
for x in combinations(range(n + k), n):
d = list(d0)
for i in x:
d[i] = "1"
if not "1011101" in "".join(d):
c += 1
yield c
def A242473(n):
return comb(2 * (p := prime(n)) - 1, p - 1) % (p**4)
def A242966_gen():
return filter(
lambda n: all(isprime(d) for d in antidivisors(n, generator=True)),
(composite(n) for n in count(1)),
)
def A244440_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if max(set(s := str(totient(n) + n))) == "1" and s.count("1") == 1
)
def A245576_gen():
return (
p
for p in (prime(i) for i in count(1))
if not (str(p).count("0") or str(p**2).count("0"))
)
def A245802_gen(startvalue=1):
return (
n for n in count(max(startvalue, 1)) if not n % sum(int(d) for d in oct(n)[2:])
)
def A246428_gen():
return (
int(n)
for n in (str(prime(x)) for x in count(1))
if isprime(int(str(sum([int(d) for d in n])) + n))
)
def A246503_gen(startvalue=1): # generator of terms
if startvalue <= 1:
yield 1
for i in count(max(startvalue, 2)):
d, n = i * i, 1
for _ in range(i):
n = (2 * n) % d
if n == 1:
yield i
break
def A246520(n):
return max(int(bin(n - k)[2:] + bin(n + k)[2:], 2) for k in range(n + 1))
def A246600(n):
return sum(1 for d in divisors(n) if n | d == n)
def A246831(n):
return int(bin(n)[2:] + bin(3 * n)[2:], 2)
def A246839_gen(): # generator of terms
p5 = 0
for n in count(5, 5):
yield from [p5] * 5
p5 += multiplicity(5, n) * n
def A247363(n):
return sorted((b + 1) ** ((2 * n - 1) - b) for b in range(2 * n - 1))[n - 1]
def A247875_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if not n % 2 or "00" in bin(n))
def A249357_gen(): # generator of terms
yield from [1, 2, 3]
l1, l2 = 3, 2
while True:
i = l1 + l2
while True:
if gcd(i, l1) == 1 and gcd(i, l2) > 1:
yield i
l2, l1 = l1, i
break
i += 1
def A249515_gen(): # generator of terms
yield 0
for g in count(1):
xp, ylist = [], []
for i in range(9 * g, -1, -1):
x = set(str(i))
if not x in xp:
xv = [int(d) for d in x]
imin = int("".join(sorted(str(i))))
if max(xv) * (g - len(x)) >= imin - sum(xv) and i - sum(xv) >= min(
xv
) * (g - len(x)):
xp.append(x)
for y in product(x, repeat=g):
if (
y[0] != "0"
and set(y) == x
and set(str(sum([int(d) for d in y]))) == x
):
ylist.append(int("".join(y)))
yield from sorted(ylist)
def A249751_gen(startvalue=3):
return (n for n in count(max(startvalue, 3)) if n == 3 or pow(n, n, n - 2) == n - 4)
def A249902_gen():
return chain(
(2,),
(
n
for n in (d**2 for d in count(1))
if isprime(2 * n - 1) and isprime(divisor_sigma(n))
),
)
def A251411_gen(): # generator of terms
n = 1
for m in A098550_gen():
if m == n:
yield n
n += 1
def A251413_gen(): # generator of terms
yield from [1, 3, 5]
l1, l2, s, b = 5, 3, 7, {}
while True:
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
yield i
l2, l1, b[i] = l1, i, True
while s in b:
b.pop(s)
s += 2
break
i += 2
def A251414_gen(): # generator of terms
yield from [1, 2, 3]
l1, l2, s, b = 5, 3, 7, {}
while True:
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
yield (i + 1) // 2
l2, l1, b[i] = l1, i, True
while s in b:
b.pop(s)
s += 2
break
i += 2
def A251415_gen(): # generator of terms
yield 1
l1, l2, s, u, l, b = 3, 2, 4, 1, 1, {}
for n in count(4):
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
l2, l1, b[i] = l1, i, 1
while s in b:
b.pop(s)
s += 1
if u * n < i * l:
yield i
u, l = i, n
break
i += 1
def A251554_gen(): # generator of terms
yield from [1, 2, 5]
l1, l2, s, b = 5, 2, 3, {5}
while True:
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
yield i
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A251561(n):
if n == 2:
return 4
q, r = divmod(n, 2)
if r:
if isprime(n):
return 2 * n
return n
if isprime(q):
return q
return n
def A251862_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if pow(-3, n, n + 3) == 3)
def A253051_gen(): # generator of terms
yield 1
c, l1, l2, s, b = 1, 2, 1, 3, set()
while True:
i = s
while True:
if not (i in b or i & l1) and i & l2:
if i & 1:
yield c
c = 0
else:
c += 1
l2, l1 = l1, i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A253147_gen():
return filter(
lambda n: n >= 256 and is_pal(intbase(sympydigits(n, 256)[-1:0:-1], 256)),
pal10_gen(),
)
def A253148_gen():
return filter(lambda n: n >= 256 and is_pal(n, 256), pal10_gen())
def A253149_gen():
return filter(
lambda n: n >= 256 and isprime(intbase(sympydigits(n, 256)[-1:0:-1], 256)),
(prime(n) for n in count(1)),
)
def A254073(n):
ndict = {}
for i in range(n):
m = pow(i, 3, n)
if m in ndict:
ndict[m] += 1
else:
ndict[m] = 1
count = 0
for i in ndict:
ni = ndict[i]
for j in ndict:
k = (1 - i - j) % n
if k in ndict:
count += ni * ndict[j] * ndict[k]
return count
def A254231_gen(): # generator of terms
yield 1
a, b, c, d = 0, 0, 1, 1
while True:
a, b, c = b, c, a + b + c
d *= c
yield d
def A254315(n):
return len(
set(
x
for l in (
[d for d in str(p)] + [d for d in str(e) if d != "1"]
for p, e in factorint(n).items()
)
for x in l
)
)
def A254756_gen(): # generator of terms
for n in count(16):
s = format(n, "x")
for i in range(1, len(s)):
if not (is_prime(int(s[i:], 16)) and is_prime(int(s[:-i], 16))):
break
else:
yield n
def A255500(n):
return (p := prime(n)) ** 4 * (p * (p * (p * (p * (p + 5) + 4) - 1) - 5) + 2) // 6
def A255501(n):
return n**4 * (n * (n * (n * (n * (n + 5) + 4) - 1) - 5) + 2) // 6
def A256437_gen(startvalue=0):
(
i
for i in count(max(startvalue, 0))
if str(i**2 + int(str(i)[::-1]) ** 2)
== str(i**2 + int(str(i)[::-1]) ** 2)[::-1]
)
def A256481(n):
if n in (6930, 50358, 56574, 72975):
return 0
if n == 0:
return 2
sn = str(n)
for i in count(1):
for j in range(1, 10, 2):
si = str(j) * i
p = int(sn + si)
if isprime(p):
return int(p)
def A256967_gen(): # generator of terms
x, d, f1, f2 = 1, 1, 1, 0
while True:
for i in range(f1):
yield x
x += d
d += 1
f1, f2 = f1 + f2, f1
def A256968_gen(): # generator of terms
count, bn, bd = 0, 1, 1
for k in count(1):
p = prime(k)
bn *= p
bd *= p - 1
while bn >= count * bd:
yield k
count += 1
def A257341_gen(): # generator of terms
m = 2
for i in count(2):
for j in range(1, i):
x = Fraction(j, i)
if x.denominator == i:
yield int(m * x) % 2
m *= 2
def A257552_gen(): # generator of terms
p = 2
while True:
q = p**2 - 2
if isprime(q):
r = q**2 - 2
if isprime(r):
s = r**2 - 2
if isprime(s):
yield p
p = nextprime(p)
def A257831(n):
return int("".join((format(int(d), "b") for d in str(n))))
def A257901_gen(startvalue=1): # generator of terms
l = []
for d in permutations("0123456789", 10):
if d[0] != "0":
d2 = int("".join(d))
if d2 >= startvalue:
d = d2
r = d2 % 5
while not r:
d2, r = divmod(d2, 5)
l.append((d2, d))
l.sort()
yield from (b for a, b in l)
def A258103(n):
"""requires 2 <= n <= 62"""
c, sm, sq = (
0,
mpz("".join([gmpy2digits(i, n) for i in range(n - 1, -1, -1)]), n),
mpz("".join(["1", "0"] + [gmpy2digits(i, n) for i in range(2, n)]), n),
)
m = isqrt(sq)
sq = m * m
m = 2 * m + 1
while sq <= sm:
if len(set(gmpy2digits(sq, n))) == n:
c += 1
sq += m
m += 2
return c
def A258774(n):
return (lambda x: x * (x + 1) + 1)(divisor_sigma(n))
def A260373_gen(): # generator of terms
yield 1
g = 1
for i in count(1):
g *= i
s = isqrt(g)
t = s**2
return t if g - t - s <= 0 else t + 2 * s + 1
def A260636_gen(): # generator of terms
b = 3
for n in count(1):
yield b % n
b = b * 3 * (3 * n + 2) * (3 * n + 1) // ((2 * n + 2) * (2 * n + 1))
def A260640_gen(): # generator of terms
b = 3
for n in count(1):
if not b % n:
yield n
b = b * 3 * (3 * n + 2) * (3 * n + 1) // ((2 * n + 2) * (2 * n + 1))
def A260674_gen():
return (p for p in (prime(n) for n in count(1)) if gcd(2**p + 1, 3**p + 1) > 1)
def A261011_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not n % (lambda x: x[0] + (0 if x[1] else 1))(integer_nthroot(n, 3))
)
def A261328_gen(): # generator of terms
bset = set()
for i in count(1):
c = i**3
for d in divisors(c, generator=True):
d2 = c // d
if d >= d2:
m, r = divmod(d + d2, 2)
if not r:
n = m - d2
if n > 0 and (m, n) not in bset and is_square(c * m + d2 * n**2):
bset.add((m, n))
yield m
def A261296_gen(): # generator of terms
bset = set()
for i in count(1):
c = i**3
for d in divisors(c, generator=True):
d2 = c // d
if d >= d2:
m, r = divmod(d + d2, 2)
if not r:
n = m - d2
if n > 0 and (m, n) not in bset and is_square(c * m + d2 * n**2):
bset.add((m, n))
yield n
def A262069_gen():
return filter(lambda n: is_pal(n, 60), pal10_gen())
def A264600(n):
return sorted(str(i)[::-1] for i in range(n + 1)).index(str(n)[::-1])
def A266727_gen(): # generator of terms
blist = [0, 1, 7]
bset = set(blist)
yield from blist
for i in count(0):
n, flag = blist[-1] + 1, False
while True:
for j in range(i + 2, 0, -1):
m = 2 * blist[j] - n
if m in bset:
break
if m < 0:
flag = True
break
else:
blist.append(n)
bset.add(n)
yield n
break
if flag:
blist.append(n)
bset.add(n)
yield n
break
n += 1
def A267310(n):
m = sum(d * divisor_sigma(d) ** (n // d) for d in divisors(n, generator=True))
return m // gcd(m, n)
def A267764_gen():
return (int(d, 4) for d in (str(i**2) for i in range(10**6)) if max(d) < "4")
def A267768_gen():
return (int(s, 8) for s in (str(i**2) for i in range(10**6)) if max(s) < "8")
def A268383_gen(): # generator of terms
b = 0
yield 0
for i in count(1):
b += 1 - len(list(filter(bool, format(i, "b").split("0")))) % 2
yield b
def A268982(n):
return n // gcd(
n, sum(d * divisor_sigma(d) ** (n // d) for d in divisors(n, generator=True))
)
def A269723_gen(): # generator of terms
blist = [0]
yield 0
while True:
x = blist + [1 - d for d in blist] * 2
blist += x
yield from x
def A271901(n):
p = prime(n)
i, a, b, c = 1, 1, 1, 2 % p
while a != 1 or b != 1 or c != 1:
i += 1
a, b, c = b, c, (a + c) % p
return i
def A272670_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if bin(n)[2:] != bin(n)[:1:-1]
and bin(n)[2:].rstrip("0") == bin(n)[:1:-1].lstrip("0")
)
def A272680(n):
if n == 0:
return 0
else:
d, nd = 1, n
while True:
x = (isqrt(nd - 1) + 1) ** 2
if x < nd + d:
return int(x)
d *= 2
nd *= 2
def A272681(n):
if n == 0:
return 0
else:
d, nd = 1, n
while True:
x = (isqrt(nd - 1) + 1) ** 2
if x < nd + d:
return int(bin(x)[2:])
d *= 2
nd *= 2
def A273190(n):
return isqrt(2 * n - 1) - isqrt(n - 1) if n > 0 else 0
def A273372_gen():
return ((10 * n + m) ** 2 for n in count(0) for m in (1, 9))
def A274944_gen():
return (
j * 10 ** (i + 1) + 10 * (j**2 + k**2) + k
for i in count(1)
for j in range(1, 10)
for k in range(10)
if 10 ** (i - 1) <= j**2 + k**2 < 10**i
)
def A274945_gen():
return (
j * 10 ** (i + 1) + 10 * (j**2 + k**2) + k
for i in count(1)
for j in range(1, 10)
for k in range(10)
if j**2 + k**2 < 10**i
)
def A274962_gen():
return chain(
(2,),
(
n
for n, s in ((d**2, divisor_sigma(d**2)) for d in count(1))
if isprime(s) and isprime(s + 2)
),
)
def A274963_gen():
return (
n
for n, s in ((d**2, divisor_sigma(d**2)) for d in count(1))
if isprime(s) and isprime(s - 2)
)
def A274967_gen(startvalue=3): # generator of terms
for n in count(max(startvalue + 1 - startvalue % 2, 3), 2):
if not isprime(n):
k = 3
while k * (k + 1) <= 2 * n:
if not (2 * (k * (k - 2) + n)) % (k * (k - 1)):
break
k += 1
else:
yield n
def A274968_gen(startvalue=4): # generator of terms
for n in count(max(startvalue + startvalue % 2, 4), 2):
k = 3
while k * (k + 1) <= 2 * n:
if not (2 * (k * (k - 2) + n)) % (k * (k - 1)):
break
k += 1
else:
yield n
def A277624_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
if not is_prime(n):
for p in primefactors(n):
if isqrt(p) * p > n:
yield n
break
def A279610(n):
return int(
"".join(str(d) for d in range((n - 1) * (n - 2) // 2 + 1, n * (n - 1) // 2 + 2))
)
def A280879_gen(): # generator of terms
t = 1
for n in count(1):
n += 1
h = totient(n)
t2 = t + h
if n % 2 and n % 6 != 3 and 2 * (n * (h * n - 2 * t2 + 1) + t2) < 1:
yield n
t = t2
def A286415_gen(): # generator of terms
for l in count(1):
for d in "123456789":
for w in product("1379", repeat=l):
s = d + "".join(w)
n = int(s)
for i in range(l):
if not isprime(int(s)):
break
s = s[-1] + s[:-1]
else:
if not isprime(int(s)):
yield n
def A286900(n):
m = nextprime(n)
return (m + n) * (m - n + 1) // 2
def A287198_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
s = str(n)
if not is_prime(n) and "0" not in s:
k = n
for i in range(len(s) - 1):
s = s[1:] + s[0]
m = mpz(s)
if is_prime(m) or gcd(k, m) > 1:
break
k *= m
else:
yield n
def A287653_gen(): # generator of terms
pq, qr, rs, s = 6, 15, 35, 7
while True:
n = pq + qr + rs
if isprime(n):
yield n
t = nextprime(s)
pq, qr, rs, s = qr, rs, s * t, t
def A296104_gen(startvalue=2):
return (n for n in count(max(startvalue, 2)) if pow(2, n, n - 1) == 3 % (n - 1))
@lru_cache(maxsize=None)
def A298406(n):
if n <= 2:
return 1
c, j = 2 * A298406(n - 1) - A298406(n - 3), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A298406(k1)
j, k1 = j2, n // j2
return c + n - j + 1
@lru_cache(maxsize=None)
def A298407(n):
if n <= 2:
return n + 1
c, j = 2 * A298407(n - 1) - A298407(n - 3), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A298407(k1)
j, k1 = j2, n // j2
return c + 2 * (n - j + 1)
@lru_cache(maxsize=None)
def A298408(n):
if n <= 2:
return 1
c, j = 2 * A298408(n - 1) - A298408(n - 3), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 * (j2 - 1) - j * (j - 1)) * A298408(k1) // 2
j, k1 = j2, n // j2
return c + (n * (n + 1) - j * (j - 1)) // 2
@lru_cache(maxsize=None)
def A298409(n):
if n <= 2:
return n + 1
c, j = 2 * A298409(n - 1) - A298409(n - 3), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 * (j2 - 1) - j * (j - 1)) * A298409(k1) // 2
j, k1 = j2, n // j2
return c + 2 * (n * (n + 1) - j * (j - 1)) // 2
def A300062_gen(): # generator of terms
yield 1
s, j = 1, 1
for i in count(2):
j, si = j + 1, str(i)
while si not in str(s + j):
j += 1
yield j
s += j
def A300078(n):
zr, zc, c = Fraction(0, 1), Fraction(0, 1), 0
cr, cc = Fraction(-5, 4) - Fraction(1, 10 ** (2 * n)), Fraction(1, 10**n)
zr2, zc2 = zr**2, zc**2
while zr2 + zc2 <= 4:
zr, zc = zr2 - zc2 + cr, 2 * zr * zc + cc
zr2, zc2 = zr**2, zc**2
c += 1
return c
def A301912_gen(): # generator of terms
n = 0
for k in count(0):
if n % 10 ** (len(str(k))) == k:
yield k
n += (k + 1) ** 3
def A269266(n):
return pow(2, n, 31)
def A308194(n):
c, x = 0, n
while x != 5:
d = divisors(x)
l = len(d)
x = d[(l - 1) // 2] + d[l // 2]
c += 1
return c
def A308736_gen(): # generator of terms
mlist = [False] * 4
for n in count(3, 2):
if mlist[0] and mlist[1] and mlist[2] and mlist[3]:
yield n
n += 2
f = factorint(n + 6)
mlist = mlist[1:] + [(len(f), sum(f.values())) == (2, 3)]
def A319302_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
for d in split("1+", bin(n)[2:]):
if isprime(len(d)):
yield n
break
def A319419(n):
s = "".join(
d[:-1] for d in split("(0+)|(1+)", bin(n)[2:]) if d not in {"", "0", "1", None}
)
return -1 if s == "" else int(s, 2)
def A320129(n):
return (
1
if n == 0
else sum(
1
for p in multiset_partitions(list(range(1, 2 * n + 1)), n)
if max(len(d) for d in p) == 2 and len(set(sum(d) for d in p)) == n
)
)
def A320261(n):
return int(
"".join(
"1" + d for d in split("(0+)|(1+)", bin(n)[2:]) if d != "" and d != None
),
2,
)
def A321294(n):
return sum(totient(d) * (n // d) ** (n + 1) for d in divisors(n, generator=True))
def A321441(n):
if n == 0:
return 1
c = 0
for i in range(n):
mi = n + i * (i + 1) // 2
for j in range(i, n):
mj = mi + j * (j + 1) // 2
for k in range(j + 1, n + 1):
r = mj - k * k
if r < 0:
break
if not r % k:
c += 1
return c
def A321536(n):
return int(
"".join(
d + d[0]
for d in split("(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)", str(n))
if d != "" and d != None
)
)
def A321537(n):
return int(
"0"
+ "".join(
d[:-1]
for d in split("(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)", str(n))
if d != "" and d != None
)
)
def A323711_gen(startvalue=9):
return (
n
for n in count(max(9, startvalue + (9 - startvalue % 9) % 9, 9))
if sorted(str(n)) == sorted(str(2 * n)) == sorted(str(3 * n))
)
def A323835(n):
mset, m, c = set(), n, 0
while True:
if m == 0 or m == 1:
return c
m = int(
"0" + "".join(d if str(2 * m).count(d) == 1 else "" for d in str(2 * m))
)
if m in mset:
return -1
mset.add(m)
c += 1
def A325230_gen(startvalue=2):
return (
n
for n, m in ((n, factorint(n)) for n in count(max(startvalue, 2)))
if len(m) == 2 and m[min(m)] == 1
)
def A327171(n):
return totient(n) * numbercore(n)
def A328330(n):
c, m = 1, sum((6, 2, 5, 5, 4, 5, 6, 3, 7, 6)[int(d)] for d in str(n))
while m != n:
c += 1
n, m = m, sum((6, 2, 5, 5, 4, 5, 6, 3, 7, 6)[int(d)] for d in str(m))
return c
def A331889_T(n, k):
if k == 1:
return n * (n + 1) // 2
if n == 1:
return int(factorial(k))
if k == 2:
return n * (n + 1) * (2 * n + 1) // 3
nk = n * k
nktuple = tuple(range(1, nk + 1))
nkset = set(nktuple)
count = int(factorial(nk))
for firsttuple in combinations(nktuple, n):
nexttupleset = nkset - set(firsttuple)
for s in permutations(sorted(nexttupleset), nk - 2 * n):
llist = sorted(nexttupleset - set(s), reverse=True)
t = list(firsttuple)
for i in range(0, k - 2):
itn = i * n
for j in range(n):
t[j] *= s[itn + j]
t.sort()
v = 0
for i in range(n):
v += llist[i] * t[i]
if v < count:
count = v
return count
def A332300(n):
x = abs(bernoulli(2 * n).p)
return 1 if x == 1 else min(primefactors(x))
def A332597(n):
return (
8
if n == 1
else 4 * (n - 1) * (8 * n - 1)
+ 8 * sum(totient(i) * (n + 1 - i) * (n + i + 1) for i in range(2, n // 2 + 1))
+ 8
* sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i) for i in range(n // 2 + 1, n + 1)
)
)
def A332598(n):
return (
22 * n - 17
if n <= 2
else 4 * (n - 1) * (3 * n - 1)
+ 12 * sum(totient(i) * (n + 1 - i) * i for i in range(2, n // 2 + 1))
+ 4
* sum(
totient(i) * (n + 1 - i) * (2 * n + 2 - i) for i in range(n // 2 + 1, n + 1)
)
)
def A332612(n):
return sum(totient(i) * (n - i) * (2 * n - i) for i in range(2, n)) // 2
def A333072(n):
f = 1
for i in range(1, n + 1):
f = lcm(f, i)
f, glist = int(f), []
for i in range(1, n + 1):
glist.append(f // i)
m = 1 if n < 2 else primorial(n, nth=False) // primorial(n // 2, nth=False)
k = m
while True:
p, ki = 0, k
for i in range(1, n + 1):
p = (p + ki * glist[i - 1]) % f
ki = (k * ki) % f
if p == 0:
return k
k += m
def A333196(n):
fs = factorint(harmonic(n).q)
return (
1
if len(fs) == 0
else prod(p ** (fs[p] // n + 1 if fs[p] % n else fs[p] // n) for p in fs)
)
def A333269_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if n == 1 or pow(17, n, n) == 2)
@lru_cache(maxsize=None)
def A333450(n):
c, j = 2 * (n + 1) - prime(n), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A333450(k1)
j, k1 = j2, n // j2
return 2 * j - c
def A333876(n):
for i in range(n):
q = 2**n - 1
for d in multiset_permutations("0" * i + "1" * (n - 1 - i)):
p = q - int("".join(d), 2)
if isprime(p):
return p
def A333877(n):
for i in range(n - 1, -1, -1):
q = 2**n - 1
for d in multiset_permutations("0" * i + "1" * (n - 1 - i)):
p = q - int("".join(d), 2)
if isprime(p):
return p
def A334045(n):
m = n | (n - 1)
return 2 ** (len(bin(m)) - 2) - 1 - m
def A334074(n):
b = comb(2 * n, n)
return sum(
Fraction(1, p) for p in range(2, n + 1) if b % p != 0 and isprime(p)
).numerator
def A334075(n):
b = comb(2 * n, n)
return sum(
Fraction(1, p) for p in range(2, n + 1) if b % p != 0 and isprime(p)
).denominator
def A336018(n):
return len(bin(n**n // (2 ** ((len(bin(n)) - 3) * n)))) - 3
def A336614(n):
c = 0
for d in product((0, 1), repeat=n * n):
M = Matrix(d).reshape(n, n)
if M * M == M.T:
c += 1
return c
def A337175(n):
return divisor_count(n) ** 2 // 4
def A337449_gen(): # generator of terms
p, q = 2, 1
for k in count(0):
if p % sum(int(d) for d in str(p)) == 0:
yield k
p, q = q, p + q
def A338136(n):
k, n2, m = 2, n**2, (n + 1) ** 2
while True:
nj = n2
while nj < m:
r = m % nj
if r > 1 and is_power(r):
return k
nj *= n
k += 1
m *= n + 1
def A338267(n):
p, q, r = prime(n) ** 2, prime(n + 1) ** 2, prime(n + 2) ** 2
return (isqrt(4 * p * q - (p + q - r) ** 2) + 2) // 4
def A340013(n):
f = factorial(n)
return (nextprime(f) - prevprime(f)) // 2
def A340869_gen(): # generator of terms
plist = [2, 3, 5, 7, 11, 13, 17, 19, 23]
for k in count(1):
d = Matrix(plist).reshape(3, 3).det()
if d >= 0 and integer_nthroot(d, 2)[1]:
yield k
plist = plist[1:] + [nextprime(plist[-1])]
def A341319(n):
return min(
(d // 2 + 1) * (e // 2 + 1)
for d, e in ((v, n**2 // v) for v in divisors(n**2) if v <= n)
)
def A341578(n):
c = min(
(d // 2 + 1) * (n**2 // (2 * d) + 1)
for d in divisors(n**2, generator=True)
if d <= n
)
return c if n % 2 else min(c, (n // 2 + 1) ** 2 - 1)
def A341709(n):
m, c = 1, 0
while n > 0:
n, b = divmod(n, 2)
c += b * int(str(m)[::-1])
m *= 2
return c
def A341721(n):
return min(
(d + 2 - (d % 2)) * (e + 2 - (e % 2)) // 4 + int((d % 2) or (e % 2)) - 1
for d, e in ((v, n // v) for v in divisors(n) if v * v <= n)
)
def A342023(n):
f = factorint(n)
for p in f:
if p <= f[p]:
return 1
return 0
def A342121(n):
a, b = sorted([n, int(bin(n)[:1:-1], 2)])
return b % a if n > 0 else 0
def A342122(n):
return int(bin(n)[:1:-1], 2) % n if n > 0 else 0
def A342123(n):
return n % int(bin(n)[:1:-1], 2) if n > 0 else 0
def A342126(n):
s = bin(n)[2:]
i = s.find("0")
return n if i == -1 else (2**i - 1) * 2 ** (len(s) - i)
def A342260(n):
k = 1
while sympydigits(k**2, n).count(n - 1) != n:
k += 1
return k
def A342545(n):
for a in range(1, n):
p, q = integer_nthroot(a * n**n, 2)
if q:
return p
l = 1
while True:
cmax = n ** (l + n + 1)
for a in range(1, n):
c = cmax
for b in product(range(1, n), repeat=l):
for d in multiset_permutations((0,) * n + b):
p, q = integer_nthroot(reduce(lambda c, y: c * n + y, [a] + d), 2)
if q:
c = min(c, p)
if c < cmax:
return c
l += 1
def A342950_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
if n % 10:
m = n
for p in (2, 3, 5, 7):
q, r = divmod(m, p)
while r == 0:
m = q
q, r = divmod(m, p)
if m == 1:
yield n
def A342996(n):
return partition(primorial(n)) if n > 0 else 1
def A343206(n):
return sum(stirling(n, i, signed=True) * bernoulli(i) for i in range(n + 1)).p
def A343675_helperf(w):
for s in w:
for t in range(int(s[-1]) + 1, 10, 2):
yield s + str(t)
def A343675_helperg(w):
for s in w:
for t in range(1 - int(s[-1]) % 2, int(s[-1]), 2):
yield s + str(t)
def A343675_gen(): # generator of terms
yield from [2, 3, 5, 7]
for l in count(1):
for d in "1379":
x = d
for i in range(1, l + 1):
x = A343675_helperg(x) if i % 2 else A343675_helperf(x)
yield from (int(p + p[-2::-1]) for p in x if isprime(int(p + p[-2::-1])))
y = d
for i in range(1, l + 1):
y = A343675_helperf(y) if i % 2 else A343675_helperg(y)
yield from (int(p + p[-2::-1]) for p in y if isprime(int(p + p[-2::-1])))
def A343676(n):
c = 0
for d in "123456789":
x = d
for i in range(1, n):
x = A343675_helperg(x) if i % 2 else A343675_helperf(x)
c += sum(1 for p in x if isprime(int(p)))
if n > 1:
y = d
for i in range(1, n):
y = A343675_helperf(y) if i % 2 else A343675_helperg(y)
c += sum(1 for p in y if isprime(int(p)))
return c
def A343677(n):
if n == 0:
return 4
c = 0
for d in "1379":
x = d
for i in range(1, n + 1):
x = A343675_helperg(x) if i % 2 else A343675_helperf(x)
c += sum(1 for p in x if isprime(int(p + p[-2::-1])))
y = d
for i in range(1, n + 1):
y = A343675_helperf(y) if i % 2 else A343675_helperg(y)
c += sum(1 for p in y if isprime(int(p + p[-2::-1])))
return c
def A343999(n):
fs = factorint(2 * n)
plist = [p ** fs[p] for p in fs]
return int(
min(
k
for k in (crt(plist, d)[0] for d in product([0, -1], repeat=len(plist)))
if k > 0
)
% 2
)
def A344589(n):
m = A011772(n)
return sum(1 for d in divisors(n) if A011772(d) < m)
def A345419(n):
return igcdex(3, prime(n))[0]
def A345423(n):
return sum(
u
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if w == 1
)
def A345424(n):
return sum(
v
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if w == 1
)
def A345425(n):
return sum(
u + v
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if w == 1
)
def A345426(n):
return sum(
u
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A345430(n):
return sum(
abs(v)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if w == 1
)
def A345431(n):
return sum(
u**2 + v**2
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if w == 1
)
def A345432(n):
return sum(
abs(u)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A345695(n):
zlist = [
z
for z in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if z[2] == 1
]
return pvariance(len(zlist) * abs(v) for u, v, w in zlist)
def A344005(n):
if n == 1:
return 1
plist = [p**q for p, q in factorint(n).items()]
return (
n - 1
if len(plist) == 1
else int(
min(
min(crt([m, n // m], [0, -1])[0], crt([n // m, m], [0, -1])[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
def A346598(n):
return sum(1 for m in range(1, n * (n + 1) + 1) if A344005(m) == n)
def A346622(n):
return (
0
if n <= 2
else A346622(n - 1) + (1 if n % 2 and len(primefactors(n)) == 2 else 0)
)
def A346623(n):
return (
0
if n <= 2
else A346623(n - 1) + (n if n % 2 and len(primefactors(n)) == 2 else 0)
)
def A346942_gen():
return (
100 * n
for n in count(99)
if n % 10 and (lambda x: x[0] == x[1] == x[2] == x[3] != x[4])(str(n**2))
)
def A347308_gen(): # generator of terms
yield 1
nset, m, c, j, i = {1}, 2, 0, 2, 1
while True:
i += 1
k = m
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
if k > c:
c = k
yield i
j = k + 1
nset.add(k)
while m in nset:
m += 1
def A347319(n):
return n * (n**2 * (2 * n - 3) + 3) + 1
def A350518(n):
q = 2
while True:
a, b = integer_nthroot(q * (n + 1) - n, 2)
if b and isprime(a):
return q
q = nextprime(q)
def A350517(n):
p = 2
while True:
a, b = divmod(p**2 + n, n + 1)
if not b and isprime(a):
return p
p = nextprime(p)
def A347755_gen(): # generator of terms
yield 1
nset, m, j = {1}, 2, 2
while True:
k = m
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
j = k + 1
nset.add(k)
yield m
while m in nset:
m += 1
def A347757_gen(): # generator of terms
yield 1
nset, m, j, i = {1}, 2, 2, 1
while True:
i += 1
k = m
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
j = k + 1
nset.add(k)
if k == m:
yield i
while m in nset:
m += 1
def A348295(n):
return sum(-1 if (isqrt(2 * k * k) - k) % 2 else 1 for k in range(1, n + 1))
def A349190_gen():
return filter(lambda n: prod(accumulate(int(d) for d in str(n))) == n, count(1))
def A004287(n):
if n > 0:
for i in range(1, 2**n):
s = bin(i)[2:]
if not int(s, 7) % n:
return int(s)
return 0
def A004288(n):
if n > 0:
for i in range(1, 2**n):
s = bin(i)[2:]
if not int(s, 8) % n:
return int(s)
return 0
def A010338_gen():
(
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and len(s) == 7
)
def A010902_gen(): # generator of terms
a, b = 14, 23
yield from [a, b]
while True:
c, d = divmod(b**2, a)
a, b = b, c + (0 if 2 * d < a else 1)
yield b
def A015945_gen(startvalue=2):
return (
n
for n in count(max(startvalue + startvalue % 2, 2), 2)
if pow(2, n, n) == n // 2 - 1
)
def A023273_gen():
return (
p
for p in (prime(n) for n in count(1))
if isprime(2 * p + 3) and isprime(4 * p + 9) and isprime(8 * p + 21)
)
def A023804_gen():
return filter(
lambda n: len(set(s := gmpy2digits(n, 9))) == len(s), range(0, 381367045)
)
def A027580_gen(): # generator of terms
for i in count(1, 2):
s = str(5 * (i * (i + 4) + 6))
if s == s[::-1]:
yield int(s)
def A029735_gen(): # generator of terms
j = 0
for i in count(0):
s = format(j, "x")
if s == s[::-1]:
yield i
j += 3 * i * (i + 1) + 1
def A029736_gen(): # generator of terms
j = 0
for i in count(0):
s = format(j, "x")
if s == s[::-1]:
yield j
j += 3 * i * (i + 1) + 1
def A030688(n):
d, nd = 10, 10 * n**2
while True:
x = isqrt(nd - 1) + 1
if not x % 10:
x += 1
x = x**2
if x < nd + d:
return x
d *= 10
nd *= 10
def A030697(n):
d, nd = 10, 10 * n**3
while True:
x = integer_nthroot(nd - 1, 3)[0] + 1
if not x % 10:
x += 1
x = x**3
if x < nd + d:
return x
d *= 10
nd *= 10
def A031598_gen():
return (
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and len(s) % 2 == 0 and s[len(s) // 2 - 1] == 100
)
def A031997_gen(startvalue=1):
return (
n
for n in count(max(startvalue + 1 - startvalue % 2, 1), 2)
if max(str(n**3)) <= "3"
)
def A033861_gen(): # generator of terms
x = 316
while True:
yield x
x += int("".join(sorted(str(x))))
def A034874_gen(): # generator of terms
a = 1
for n in count(2):
yield a
a = n * int(str(a)[::-1])
def A035057_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if "1" not in str(2**n))
def A036433_gen(startvalue=1): # generator of terms
for i in count(max(startvalue, 1)):
d = divisor_count(i)
if d < 10 and str(d) in str(i):
yield i
def A037255(n):
return n * (n * (n * (n - 2) + 7) + 2) // 8
def A048055(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = sum(divisors(n))
if not s % 2 and 2 * n <= s and (s - 2 * n) / 2 == sum(primefactors(n)):
yield n
def A048335_gen():
return chain((0,), (int(d * l, 11) for l in count(1) for d in "123456789a"))
def A048336_gen():
return chain((0,), (int(d * l, 12) for l in count(1) for d in "123456789ab"))
def A048337_gen():
return chain((0,), (int(d * l, 13) for l in count(1) for d in "123456789abc"))
def A048338_gen():
return chain((0,), (int(d * l, 14) for l in count(1) for d in "123456789abcd"))
def A048339_gen():
return chain((0,), (int(d * l, 15) for l in count(1) for d in "123456789abcde"))
def A048889_gen():
return (
m
for m in (
int(e + "".join(d))
for l in count(1)
for e in "1689"
for d in product("01689", repeat=l)
)
if m % 10
and not isprime(m)
and isprime(int(str(m)[::-1].translate("".maketrans("69", "96"))))
)
def A051640(n):
m = 0
while True:
for b in range(2, n + 1):
if b - 1 not in sympydigits(m, b)[1:]:
break
else:
return m
m += 1
def A052191(n):
k = 0
while True:
k += n
x = split("(0+|1+|2+|3+|4+|5+|6+|7+|8+|9+)", str(k))
for d in x:
if len(d) == 1:
break
else:
return k
def A053547(n):
s = int("".join(str(m) for m in range(n, 0, -1)))
for i in count(1):
s *= 10
for j in range(1, 10**i, 2):
x = s + j
if isprime(x):
return x
def A055227(n):
return s if (f := factorial(n)) - (s := isqrt(f)) * (s + 1) <= 0 else s + 1
def A055227_gen(): # generator of terms
yield 1
g = 1
for i in count(1):
g *= i
s = isqrt(g)
yield s if g - s * (s + 1) <= 0 else s + 1
def A056825_gen(): # generator of terms
nset = set()
for n in count(1):
cf = continued_fraction_periodic(0, 1, n)
if len(cf) > 1:
pal = tuple(cf[1][:-1])
if pal not in nset:
yield n
nset.add(pal)
def A057683_gen(startvalue=0):
return (
n
for n in count(max(startvalue, 0))
if isprime(n**2 + n + 1)
and isprime(n**3 + n + 1)
and isprime(n**4 + n + 1)
)
def A059000_gen(): # generator of terms
for i in count(0):
if i % 10:
p = int(str(i**5)[::-1])
if isprime(p):
yield p
def A060474(n):
return (n + 1) // gcd(n + 1, totient(n))
def A062936_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = str(n * int(str(n)[::-1]))
if s == s[::-1]:
yield n
def A063569(n):
m, k, s = 1, 6, str(n)
while s not in str(k):
m += 1
k *= 6
return m
def A063570(n):
m, k, s = 1, 7, str(n)
while s not in str(k):
m += 1
k *= 7
return m
def A065914(n):
pm = primorial(n)
return primepi(3 * pm // 2 - 1) - primepi(pm // 2 - 1)
def A066713(n):
m = 2**n
return int("".join(sorted(str(m + int(str(m)[::-1])))))
def A067770_gen(): # generator of terms
yield from [1, 1]
c = 1
for n in count(2):
c = c * (4 * n - 2) // (n + 1)
yield c % (n + 2)
def A071837_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
fp, fe = zip(*factorint(n).items())
if sum(fp) == sum(fe) and isprime(sum(fe)) and all([isprime(e) for e in fe]):
yield n
def A073931_gen(startvalue=1):
return filter(lambda n: antidivisor_sigma(n) == 2 * n, count(max(startvalue, 1)))
def A076634(n):
y = Poly(prod(2 * symbolx + i for i in range(1, n + 1))).all_coeffs()[::-1]
return y.index(max(y))
def A077441(n):
if n > 0:
k = 0
while True:
m = k
for i in range(n):
s = gmpy2digits(m, 4)
if s == s[::-1]:
break
m += int(s[::-1], 4)
else:
s = gmpy2digits(m, 4)
if s == s[::-1]:
return k
k += 1
else:
return 0
def A078266(n):
s = "".join(str(i) for i in range(1, n + 1))
return sum(int(d) for d in s) * (10 ** len(s) - 1) // (9 * len(s))
def A083178(n):
return (
1
if n == 1
else (2 * 10 ** ((n + 2) // 3) + (63 * (n % 3) ** 2 - 129 * (n % 3) - 2)) // 6
)
def A083289(n):
a, b = divmod(n, 2)
c, d = 10**n, 10**a
if b == 0:
return nextprime(d) ** 2 - c
k = 0
while True:
fs = factorint(c + k, multiple=True)
if len(fs) == 2 and min(fs) >= d:
return k
k += 1
def A085647_gen(startvalue=2):
return filter(
lambda n: len(f := factorint(n)) == 2 == sum(f.values())
and len(str((s := list(f.keys()))[0])) == len(str(s[1])),
count(max(startvalue, 2)),
)
def A087304(n):
i, p = 2, prod(int(d) for d in str(n) if d != "0")
while (max(str(i)) == "1" and str(i).count("1") == 1) or prod(
int(d) for d in str(i * n) if d != "0"
) != p:
i += 1
return i * n
def A090392(n):
return n * (n * (n * (n * (n * (n + 45) + 925) + 11475) + 92314) + 413640) // 720
def A090393(n):
return (
n
* (
n * (n * (n * (n * (n * (n + 63) + 1855) + 34125) + 438424) + 3980172)
+ 20946960
)
// 5040
)
def A090394(n):
return (
n
* (
n
* (
n * (n * (n * (n * (n * (n + 84) + 3346) + 84840) + 1550689) + 21632436)
+ 224782284
)
+ 1377648720
)
// 40320
)
def A092679_gen(startvalue=0):
return filter(
lambda k: antidivisor_count(3 * 2**k) == 1, count(max(startvalue, 0))
)
def A092680_gen():
return filter(lambda n: antidivisor_count(n) == 1, (3 * 2**k for k in count(0)))
def A096357(n):
return lcm(*antidivisors(n, generator=True))
def A097228_gen():
return chain(
(27, 38),
(1000 * (10**k - 1) // 9 + d for k in count(0) for d in (127, 138, 289, 298)),
)
def A104174(n):
return (lambda x: x.p % x.q)(harmonic(n))
def A109350_gen(startvalue=3):
return filter(lambda n: isprime(antidivisor_sigma(n)), count(max(startvalue, 3)))
def A110068_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if nextprime(10 ** (n - 1)) - 10 ** (n - 1) == primepi(n)
)
def A113484(n):
for k in count(n + 1):
if gcd(k, n) == 1 and not isprime(k):
return k
def A116988(n):
return sum(int(d) for d in str(factorial(10**n)))
def A117057_gen():
return filter(
lambda p: "0" not in (s := str(p)) and p % prod(int(d) for d in s) == 0,
pal10_gen(),
)
def A349325(n):
x, c, n2, n3 = n, 1, 2 * n, 3 * n
while x > 1:
if x % 2:
c += int(n3 > 3 * x >= n2)
x = (3 * x + 1) // 2
else:
c += int(n < x < n2)
x //= 2
return c
def A350514(n):
return (
1
if n == 0
else max(
prod(1 - symbolx ** prime(i) for i in range(1, n + 1)).as_poly().coeffs()
)
)
def A117769_gen(): # generator of terms
a, b = 2, 1
for i in count(0):
if prod(int(d) for d in str(b)) in {0, 1, 2, 3, 5, 8, 21, 144}:
yield b
a, b = b, a + b
def A117770_gen(): # generator of terms
yield 0
a, b = 1, 1
for i in count(0):
if prod(int(d) for d in str(b)) in {0, 1, 2, 3, 5, 8, 21, 144}:
yield b
a, b = b, a + b
def A350278(n):
for m in count(1):
if A349325(m) == n:
return m
def A350277_gen(): # generator of terms
c = 0
for n in count(1):
m = A349325(n)
if m > c:
yield n
c = m
def A127741_gen(): # generator of terms
blist, b = [1], 1
for n in count(1):
blist = list(accumulate([b] + blist))
b = blist[-1]
yield blist[-2] * n
def A128437(n):
return harmonic(n).p // n
def A132174(n):
if n == 1:
return 1
if n == 2:
return 5
h, m = divmod(n - 3, 5)
return (
(382 * 2 ** (5 * h + m) - 10 * 2**m) // 31
- 7 * h
- m
- (1 if m == 3 else (-1 if m == 4 else 2))
)
def A136845_gen(): # generator of terms
yield from [0, 1]
for l in count(0):
for a in ("1", "3", "5", "8"):
for b in product("01358", repeat=l):
for c in ("0", "1", "5"):
n = int("".join([a] + list(b) + [c]))
if set(str(n * n)) <= {"0", "1", "3", "5", "8"}:
yield n
def A137146_gen():
return (
n
for n in (
int("".join(d)) for l in range(1, 6) for d in product("5678", repeat=l)
)
if set(str(n**2)) <= set("5678")
)
def A137401(n):
ndict = {}
for i in range(1, n):
m = pow(i, 3, n)
if m in ndict:
ndict[m] += 1
else:
ndict[m] = 1
count = 0
for i in ndict:
ni = ndict[i]
for j in ndict:
k = (i + j) % n
if k in ndict:
count += ni * ndict[j] * ndict[k]
return count
def A138091_gen(): # generator of terms
m = [
6227020800,
44068147200,
181142438400,
564307430400,
1475073815040,
3408641107200,
7182564530400,
14081919023520,
26048741640120,
45924510262992,
77755456075656,
127171611204708,
201851662963039,
312086923782438,
]
for n in count(1):
for i in range(13):
m[i + 1] += m[i]
if isprime(m[-1]):
yield n
def A140868(n):
f = lambda n: n + isqrt(2 * n**2)
return f(f(n))
def A141263_gen(): # generator of terms
p = 1
while True:
p = nextprime(p)
ps = int(str(p)[::-1])
if p <= ps and isprime(ps):
yield p
@lru_cache(maxsize=None)
def A143443(n):
if n == 0:
return 0
c, j = n, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A143443(k1) // k1
j, k1 = j2, n // j2
return n * (j - c)
def A145643(n):
return (
1
if n <= 1
else prod(p ** (e % 3) for p, e in factorint(prod(range(n, 0, -2))).items())
)
def A155148_gen(): # generator of terms
m = [24, -36, 14, -1, 0]
for n in count(1):
for i in range(4):
m[i + 1] += m[i]
if len(set(str(m[-1]))) == 2:
yield n
def A155149_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if len(set(str(n**4))) == 3)
def A156200_gen():
return (
int("".join(d))
for l in count(4)
for d in product("0689", repeat=l)
if d[0] != "0" and len(set(d)) == 4 and is_prime(int("".join(d)))
)
def A157712(n):
if n == 1:
return 11
if n == 2:
return 0
p = prime(n)
l = p
while True:
for i in combinations(range(l), l - p):
s = ["1"] * l
for x in i:
s[x] = "0"
q = int("".join(s))
if isprime(q):
return q
l += 1
def A158214_gen(): # generator of terms
for i in count(2):
if i % 6 == 1 or i % 6 == 5:
i2 = i // 2
l = i2
flag = True
while flag:
dlist = "0" * (l - i2) + "1" * i2
for d in multiset_permutations(dlist):
s = "".join(d)
n = int(s + "1" + s[::-1])
if isprime(n):
yield n
flag = False
break
else:
l += 1
def A161502(n):
s = bin(n)[2:]
if s == s[::-1]:
return 0
for i in range(1, len(s)):
if s[i:] == s[-1 : i - 1 : -1]:
return i
def A161721_gen(startvalue=2):
p = max(nextprime(startvalue - 1), 2)
while True:
q = int(str(p)[::-1])
if is_pal(p * q) and isprime(q):
yield p
p = nextprime(p)
def A162555_gen(): # generator of terms
bset, s = set(), 0
for i in count(1):
j, si = 1, str(i)
while si not in str(s + j) or j in bset:
j += 1
yield j
bset.add(j)
s += j
@lru_cache(maxsize=None)
def A162943(n):
if n == 0:
return 2
c, j = n, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (4 - len(bin(A162943(k1))))
j, k1 = j2, n // j2
return 2 ** (1 + c - j)
def A163498_gen():
return (
prime(n) for n in count(1) if isprime(int(bin(prime(n)).replace("1", "01"), 2))
)
def A163499_gen():
return (
int(bin(prime(n)).replace("1", "01"), 2)
for n in count(1)
if isprime(int(bin(prime(n)).replace("1", "01"), 2))
)
def A173207_gen(): # generator of terms
a, b = 1, 2
while True:
if max(factorint(b).values()) == 2:
yield b
a, b = b, a + b
def A175017_gen(startvalue=2): # generator of terms
p = max(nextprime(startvalue - 1), 2)
while True:
s = str(p)
if "13" in s and sum(int(d) for d in s) == 13:
yield p
p = nextprime(p)
def A175345_gen(): # generator of terms
(c,) = 1
for k in count(1):
if is_square(c):
yield k
c += divisor_count(k)
def A180481(n):
p = prime(n)
q = nextprime(p)
while True:
if (
isprime(p * (q - p) + q)
and isprime(p * (q - p) - q)
and isprime(q * (q - p) + p)
and isprime(q * (q - p) - p)
):
return q
n += 1
q = nextprime(q)
def A180484_gen():
return (
int(n)
for n in (str(x) for x in count(1))
if not (n.count("0") or int(n) ** 2 * len(n) % prod(int(d) for d in n) ** 2)
)
def A181373(n):
s, p, l = "", prime(n), 0
for m in count(1):
u = str(m)
s += u
l += len(u)
t = s
if not int(t) % p:
for i in range(l - 1):
t = t[1:] + t[0]
if int(t) % p:
break
else:
return m
def A186774(n):
if sum(int(d) for d in str(n)) == 1:
return 0
sn, k = str(n + 1), 1
while sn not in str(k):
k *= n
return k
def A187394(n):
return 4 * n - 1 - isqrt(8 * n**2)
def A188061_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if pow(
isqrt(n) if is_square(n) else n,
int(divisor_sigma(n, 0)) // (1 if is_square(n) else 2),
int(divisor_sigma(n, 1)),
)
== 1
)
def A188082(n):
return isqrt(3 * (n + 1) ** 2) - isqrt(3 * n**2) - 1
def A192273_gen(startvalue=3): # generator of terms
for n in count(max(startvalue, 3)):
d = antidivisors(n)
s = sum(d)
if not s % 2 and max(d) <= s // 2:
for x in range(1, 2 ** len(d)):
if sum(Subset.unrank_binary(x, d).subset) == s // 2:
yield n
break
def A194152(n):
return 5 * n + isqrt(20 * n**2)
def A198244_gen(): # generator of terms
m = [
3628800,
-15966720,
28828800,
-27442800,
14707440,
-4379760,
665808,
-42240,
682,
0,
1,
]
for n in count(1):
for i in range(10):
m[i + 1] += m[i]
if not isprime(n) and isprime(m[-1]):
yield m[-1]
def A199303_gen():
return (
n
for n in (
int(t + "".join(s))
for l in count(0)
for t in "13"
for s in product("013", repeat=l)
)
if isprime(n) and isprime(int(str(n)[::-1]))
)
def A199328_gen():
return (
n
for n in (
int(t + "".join(s))
for l in count(0)
for t in "18"
for s in product("018", repeat=l)
)
if isprime(n) and isprime(int(str(n)[::-1]))
)
def A199302_gen():
return (
n
for n in (
int(t + "".join(s))
for l in count(0)
for t in "12"
for s in product("012", repeat=l)
)
if isprime(n) and isprime(int(str(n)[::-1]))
)
def A349862(n):
return max(comb(n - 2 * k, k) for k in range(n // 3 + 1))
def A210698(n):
if n % 3 == 0:
return 11 * n**4 // 27
elif n % 3 == 1:
return (11 * n**4 - 8 * n**3 + 6 * n**2 + 4 * n + 14) // 27
else:
return (11 * n**4 - 16 * n**3 + 24 * n**2 + 32 * n + 8) // 27
def A211071(n):
if n % 3 == 0:
return 8 * n**4 // 27
elif n % 3 == 1:
return (8 * n**4 + 4 * n**3 - 3 * n**2 - 2 * n - 7) // 27
else:
return (8 * n**4 + 8 * n**3 - 12 * n**2 - 16 * n - 4) // 27
def A213239_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if sum(
sum(int(x) for x in str(d))
for d in range(2, n)
if n % d and 2 * n % d in [d - 1, 0, 1]
)
== sum(int(x) for x in str(n))
)
def A350473(n):
return fibonacci(n + 1) ** 3 - fibonacci(n - 1) ** 3
def A214648_gen(): # generator of terms
s, c, d = 0, 0, -1
while True:
k = 2
q = 4 * (k * (k * (k + c) + d)) // 3 + 1
while not is_square(q):
k += 1
q = 4 * (k * (k * (k + c) + d)) // 3 + 1
yield k
s += k
c, d = 3 * s, 3 * s**2 - 1
def A214697(n):
k, a1, a2, m = 2, 36 * n, 36 * n**2 - 12, n * (72 * n + 144) + 81
while int(round(sqrt(m))) ** 2 != m:
k += 1
m = k * (k * (12 * k + a1) + a2) + 9
return k
def A216394(n):
if n == 1:
return 1
c = 0
for i in range(2 ** (n - 1) + 1, 2**n):
s1, s2 = sorted(str(i)), sorted(str(totient(i)))
if len(s1) == len(s2) and s1 == s2:
c += 1
return c
def A217175(n):
if n == 1:
return 0
else:
l, y, x = [str(d) * n for d in range(10)], 0, 1
for m in count(1):
s = str(x)
for k in range(10):
if l[k] in s:
return k
y, x = x, y + x
def A217176(n):
if n == 1:
return 2
else:
l, y, x = [str(d) * n for d in range(10)], 2, 1
for m in count(1):
s = str(x)
for k in range(10):
if l[k] in s:
return k
y, x = x, y + x
def A218035(n):
return (
4
if n == 1
else (n**3 - 9 * n**2 + 59 * n - 3) // 24
if n % 2
else (n**3 - 6 * n**2 + 32 * n + 48) // 48
)
def A343098(n):
return (
1
if n == 0
else (
n * (n * (n * (6 * n - 52) + 510) + 904)
+ 1491
+ (-1 if n % 2 else 1) * (n * (n * (42 - 4 * n) - 296) + 45)
)
// 768
)
def A224252_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if n != int(str(n)[::-1])
and primefactors(n) == primefactors(int(str(n)[::-1]))
and sorted(factorint(n).values())
== sorted(factorint(int(str(n)[::-1])).values())
)
def A253631_gen():
return filter(
lambda n: isprime(n) and is_pal(n**2), (int(bin(m)[2:]) for m in pal_gen(b=2))
)
def A227491(n):
return (
2**n * (2**n * (526338 * n**2 - 2685555 * n + 4790367) - 5719932) // 8
+ 116340
)
def A229134_gen(): # generator of terms
for i in count(0):
m, m2, j, k = 2, 4, 4 * i**2 + 1, 2 * i**2
while k >= m2 + m:
if is_square(j - m2):
yield i**2
break
m2 += 2 * m + 1
m += 1
def A229972_gen(startvalue=1):
return (
i
for i in count(max(startvalue, 1))
if not isprime(i) and (integer_nthroot(i, 3)[1] or divisor_count(i) % 3 == 2)
)
def A236359_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
d = divisors(n)
d.pop()
ld = len(d)
if sum(d) >= n:
s, j = d[0], 1
for i in range(ld - 1):
while s < n and j < ld:
s += d[j]
j += 1
if s == n:
yield n
break
j -= 1
s -= d[i] + d[j]
def A236513(n):
l, k, c = n - 1, 2**n, 0
while True:
for d in combinations(range(l - 1, -1, -1), l - n + 1):
m = k - 1 - sum(2 ** (e) for e in d)
if isprime(m):
c += 1
if c == n:
return m
l += 1
k *= 2
def A240924_gen():
return (1 + (n * n - 1) % 9 for n in count(1, 2) if n % 3 and n % 5)
def A240983_gen():
(2**p * p * p for p in (prime(n) for n in count(1)) if isprime(p + 2))
def A241989_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not n % sum(int(d, 16) for d in hex(n)[2:])
)
def A242018_gen(): # generator of terms
blist = [0, 0, 1]
yield from blist
while True:
x = blist[len(blist) // 2 :]
yield from x
blist += x
def A242107_gen(): # generator of terms
blist = [0, 1, 1, 1, 1, -1]
yield from blist
for n in count(6):
blist = blist[1:] + [
(-blist[-1] * blist[-4] + blist[-2] * blist[-3]) // blist[-5]
]
yield blist[-1]
def A242108_gen():
return (abs(n) for n in A242107_gen())
def A243102_gen(startvalue=1):
return (
int(n)
for n in (str(x) for x in count(max(startvalue, 1)))
if not n.count("0")
and sorted(str(int(n) + prod(int(d) for d in n))) == sorted(n)
)
def A243318_gen(): # generator of terms
m = [
3628800,
-16692480,
31651200,
-31827600,
18163440,
-5826240,
971232,
-69720,
1362,
-2,
-1,
]
for n in count(1):
for i in range(10):
m[i + 1] += m[i]
if isprime(m[-1]):
yield n
def A244423_gen():
return filter(
lambda p: not isprime(p) and is_pal(divisor_prod(p)), islice(pal_gen(), 1, None)
)
def A244428_gen(startvalue=1):
return (
i
for i in count(max(startvalue, 1))
if (integer_nthroot(i, 3)[1] or not divisor_sigma(i, 0) % 3)
and integer_nthroot(int(divisor_sigma(i, 1)), 3)[1]
)
def A007955(n):
return divisor_prod(n)
def A244466_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if n == 1
or (
not isprime(n)
and max(factorint(totient(n)).values()) < 2
and (-1) ** len(primefactors(totient(n))) == 1
)
)
def A244551_gen(): # generator of terms
for p in pal_gen():
l = len(str(p))
for i in range(1, l * 9 + 1):
n = p - i
if n > 0:
if sum((int(d) for d in str(n))) == i:
s = str(n - i)
if s == s[::-1]:
yield n
def A244915_gen(): # generator of terms
yield 1
bset, c = set(), 1
while True:
a, b = 1, 1 + c**2
while not isprime(b) or b in bset:
b += 2 * a + 1
a += 1
bset.add(b)
yield a
c = a
def A244959(n):
if n > 0:
for i in range(1, 2**n):
x = int(bin(i)[2:], 8)
if not x % n:
return x
return 0
def A245042_gen():
return filter(
isprime, ((k**2 + 4) // 5 for k in count(0) if (k**2 + 4) % 5 == 0)
)
def A245045_gen():
return filter(
isprime, ((k**2 + 2) // 6 for k in count(0) if (k**2 + 2) % 6 == 0)
)
def A245085(n):
p, f, fv = prime(n), 1, {}
for i in range(2, p):
f = (f * i) % p
if f in fv:
return i - 1
else:
fv[f] = i
return p - 1
def A245644_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not sum(divisors(n**3)) % divisor_count(n**3)
)
def A245763_gen():
return (
int(n)
for n in (str(prime(x)) for x in count(1))
if isprime(int(str(sum(int(d) for d in n)) + n))
and isprime(int(n + str(sum(int(d) for d in n))))
)
def A245909(n):
return len(primefactors(prime(n) ** 3 - 1))
def A246135_gen(): # generator of terms
blist = []
for n in range(1, 9):
for m in range(n - 1, -1, -1):
l = "".join(str(d) for d in range(n, m - 1, -1))
p = int(l + l[-2::-1], 9)
if isprime(p):
blist.append(p)
for m in range(n + 1, 9):
l = "".join(str(d) for d in range(n, m + 1))
p = int(l + l[-2::-1], 9)
if isprime(p):
blist.append(p)
yield from sorted(blist)
def A246136_gen(): # generator of terms
blist = []
for n in range(1, 8):
for m in range(n - 1, -1, -1):
l = "".join(str(d) for d in range(n, m - 1, -1))
p = int(l + l[-2::-1], 8)
if isprime(p):
blist.append(p)
for m in range(n + 1, 8):
l = "".join(str(d) for d in range(n, m + 1))
p = int(l + l[-2::-1], 8)
if isprime(p):
blist.append(p)
yield from sorted(blist)
def A246337_gen():
return (
n
for n, s in ((n, hex(n)[2:]) for n in islice(pal_gen(16), 1, None))
if "0" not in s
and not ((n % sum(int(d, 16) for d in s)) or (n % prod(int(d, 16) for d in s)))
)
def A246338_gen():
return (
n
for n, s in ((n, oct(n)[2:]) for n in islice(pal_gen(8), 1, None))
if "0" not in s
and not ((n % sum(int(d, 8) for d in s)) or (n % prod(int(d, 8) for d in s)))
)
def A246601(n):
return sum(d for d in divisors(n, generator=True) if n | d == n)
def A246701(n):
return max(
int(bin(n + 1 - k)[2:] + bin(n + 1 + k)[2:], 2) for k in range(n + 2)
) - max(int(bin(n - k)[2:] + bin(n + k)[2:], 2) for k in range(n + 1))
def A092517(n):
return divisor_count(n) * divisor_count(n + 1)
def A246817_gen(): # generator of terms
p5 = 0
for n in count(5, 5):
yield p5
p5 += multiplicity(5, n) * n
def A246874_gen():
return (
p
for p in (prime(n) for n in count(1))
if all(isprime(p - m * m) for m in range(2, 10, 2))
)
def A246971_gen(): # generator of terms
for n in count(0):
for k in range(n, -1, -1):
c, d0 = 0, ["0"] * (n + k)
for x in combinations(range(n + k), n):
d = list(d0)
for i in x:
d[i] = "1"
if not "0100010" in "".join(d):
c += 1
yield c
def A247128_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if (n % 22) in {0, 5, 9, 13, 17})
def A247221_gen(startvalue=0):
return (
n for n in count(max(startvalue, 0)) if pow(2, n, 2 * n * n + 1) == 2 * n * n
)
def A247348_gen():
return (
p
for p in (5 * prime(n) + 4 for n in count(1))
if not ((p - 1) % 2 or (p - 2) % 3 or (p - 3) % 4)
and isprime(p)
and isprime((p - 1) // 2)
and isprime((p - 2) // 3)
and isprime((p - 3) // 4)
)
def A247855(n):
return hermite(10, n)
def A247850(n):
return hermite(5, n)
def A247854(n):
return hermite(9, n)
def A247853(n):
return hermite(8, n)
def A247852(n):
return hermite(7, n)
def A247851(n):
return hermite(6, n)
def A163323(n):
return hermite(4, n)
def A163322(n):
return hermite(3, n)
def A348634(n):
return (
n
* (n - 2)
* (n - 1)
* (
n * (n * (n * (n * (n * (n * (n - 17) + 167) - 965) + 3481) - 7581) + 9060)
- 4608
)
// 120
)
def A248323_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if len(
list(
re.finditer(
"(?=" + str(n) + ")", "".join([str(d) for d in divisors(n)])
)
)
)
> 1
)
def A248889_gen():
return (n for n in pal10_gen() if is_pal(n, 18))
def A249517_gen(): # generator of terms
yield 0
for g in count(1):
xp, ylist = [], []
for i in range(9 * g, -1, -1):
x = set(str(i))
if not (("0" in x) or (x in xp)):
xv = [int(d) for d in x]
imin = int("".join(sorted(str(i))))
if max(xv) * (g - len(x)) >= imin - sum(xv) and i - sum(xv) >= min(
xv
) * (g - len(x)):
xp.append(x)
for y in product(x, repeat=g):
if set(y) == x:
yd = [int(d) for d in y]
if set(str(sum(yd))) == x == set(str(prod(yd))):
ylist.append(int("".join(y)))
yield from sorted(ylist)
def A249689_gen(): # generator of terms
l1, l2, s, b = 2, 1, 3, set()
for n in count(3):
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) == 1:
l2, l1 = l1, i
b.add(i)
if l2 > l1 and n % 3 == 1:
yield (n - 1) // 3
while s in b:
b.remove(s)
s += 1
break
i += 1
def A249780(n):
return max(p := primefactors(2**n - 1)) * min(p)
def A249951_gen(): # generator of terms
m = [362880, -1229760, 1607760, -1011480, 309816, -40752, 1584, -4, 1]
for n in count(1):
for i in range(8):
m[i + 1] += m[i]
if isprime(m[-1]):
yield n
def A250127_gen(): # generator of terms
yield 1
l1, l2, s, u, l, b = 3, 2, 4, 1, 1, {}
for n in count(4):
i = s
while True:
if not i in b and gcd(i, l1) == 1 and gcd(i, l2) > 1:
l2, l1, b[i] = l1, i, 1
while s in b:
b.pop(s)
s += 1
if u * n < i * l:
yield n
u, l = i, n
break
i += 1
def A250984_gen(): # generator of terms
m = -1
for i in count(3):
if (v := A247190(i)) > m:
yield v
m = v
def A250985_gen(): # generator of terms
m = -1
for i in count(3):
if (v := A247190(i)) > m:
yield i
m = v
def A251360_gen(): # generator of terms
p = 3
for n in count(2):
q, fn = prime(n + 1), factorint(n)
m = int("".join(str(d) * fn[d] for d in sorted(fn)))
if p <= m < q:
yield m
p = q
def A251756_gen(): # generator of terms
yield 0
l, s, b = 0, 1, {}
while True:
i = s
while True:
if not i in b:
m = gcd(i, l)
if not (m == 1 or isprime(m)):
yield i
l, b[i] = i, True
while s in b:
b.pop(s)
s += 1
break
i += 1
def A252606_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if pow(2, n, n + 2) == n)
def A253047(n):
if n <= 2:
return n
if n == 3:
return 7
q2, r2 = divmod(n, 2)
if r2:
q3, r3 = divmod(n, 3)
if r3:
if isprime(n):
m = primepi(n)
if isprime(m):
return prime(2 * m)
x, y = divmod(m, 2)
if not y:
if isprime(x):
return prime(x)
return n
if isprime(q3):
return 2 * prevprime(q3)
return n
if isprime(q2):
return 3 * nextprime(q2)
return n
def A253084_T(n, k):
return int(not (~(n + k) & (n - k)) | (~n & k))
def A253264_gen(): # generator of terms
p = 2
while True:
q = p**2 - 2
if isprime(q):
r = q**2 - 2
if isprime(r):
s = r**2 - 2
if isprime(s) and isprime(s**2 - 2):
yield p
p = nextprime(p)
def A253576_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if set(str(n)) & set(str(n**7)) == set() and isprime(n)
)
def A253577_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if set(str(n)) & set(str(n**8)) == set() and isprime(n)
)
def A253606_gen(startvalue=1):
return (
n for n in count(max(startvalue, 1)) if set(str(n)) & set(str(n**8)) == set()
)
def A254232_gen(): # generator of terms
yield 2
a, b, c, d = 3, 0, 2, 2
while True:
a, b, c = b, c, a + b
d *= c
yield d
def A254687(n):
y, x, n2 = 0, 2, 2 * n
while x < n:
if isprime(n2 - x) and isprime(n2 - 2 * x - 1):
y += 1
x = nextprime(x)
return y
def A254688(n):
y, x, n2 = 0, 2, 2 * n
while x < n:
if isprime(n2 - x) and isprime(n2 - 2 * x + 1):
y += 1
x = nextprime(x)
return y
def A255132_gen(): # generator of terms
yield from [1, 1]
c, s = {}, 3
for n in count(2):
for p, e in factorint(4 * n - 2).items():
if p in c:
c[p] += e
else:
c[p] = e
for p, e in factorint(n + 1).items():
if c[p] == e:
del c[p]
else:
c[p] -= e
if n == s:
c2 = prod(e + 1 for e in c.values())
yield c2
s = 2 * s + 1
def A255133_gen(): # generator of terms
yield from [1, 1]
c, s = {}, 3
for n in count(2):
for p, e in factorint(4 * n - 2).items():
if p in c:
c[p] += e
else:
c[p] = e
for p, e in factorint(n + 1).items():
if c[p] == e:
del c[p]
else:
c[p] -= e
if n == s:
c2 = 2 ** len(c)
yield c2
s = 2 * s + 1
def A255194_gen(): # generator of terms
p, p2 = 2, 3
for n in count(1):
if p2 - p > 6:
for i in range(1, 7):
fs = factorint(p + i)
if len(fs) > 3 or sum(list(fs.values())) != 3:
break
else:
yield n
p, p2 = p2, nextprime(p2)
def A255244_gen(): # generator of terms
for n in count(1):
s0 = s2 = 1
for p, e in factorint(n).items():
s0 *= e + 1
s2 *= (p ** (2 * (e + 1)) - 1) // (p**2 - 1)
q, r = divmod(s2, s0)
if not (r or q % n):
yield n
def A255245_gen(): # generator of terms
for n in count(2):
s0 = s2 = 1
for p, e in factorint(n).items():
s0 *= e + 1
s2 *= (p ** (2 * (e + 1)) - 1) // (p**2 - 1)
q, r = divmod(s2 - n**2, s0 - 1)
if not (r or q % n):
yield n
def A255484(n):
return prod(0 if ~n & k else prime(k + 1) for k in range(n + 1))
def A256048(n):
sn = str(n)
for p in pal10_odd_range_gen(len(sn) + 2):
if sn in str(p)[1:-1] and isprime(p):
return p
def A256112_helper(n, b):
if n == 1:
t = list(range(b))
for i in range(1, b):
u = list(t)
u.remove(i)
yield i, u
else:
for d, v in A256112_helper(n - 1, b):
for g in v:
k = d * b + g
if not k % n:
u = list(v)
u.remove(g)
yield k, u
def A256112_gen():
return (a * k + b[0] for k in count(2) for a, b in A256112_helper(k - 1, k))
def A256480(n):
sn = str(n)
if not (n % 2 and n % 5):
return 0
for i in count(1):
for j in range(1, 10):
si = gmpy2digits(j, 10) * i
p = int(si + sn)
if isprime(p):
return p
def A256635(n):
k = 1
while sum(int(d) for d in str(divisor_sigma(k))) != n:
k += 1
return k
def A257299_gen(): # generator of terms
blist = []
for n in permutations("123456789", 9):
x = 0
for d in n:
q, r = divmod(x, int(d))
if r:
break
x = int(d + str(q))
else:
blist.append(x)
yield from sorted(blist)
def A257864_gen(): # generator of terms
g, h = 105, 128
for i in count(9, 2):
g *= i
if isprime(g - h):
yield i
def A257342(n):
m, y, t, = (
2,
Fraction(0, 1),
10 ** (n + 1),
)
for i in count(2):
for j in range(1, i):
x = Fraction(j, i)
if x.denominator == i:
y += Fraction(int(m * x) % 2, m)
m *= 2
if m > 10000 * t:
break
return int(y * t) % 10
def A258574_gen(): # generator of terms
a, b = 0, 2
for n in count(0):
if max(factorint(b).values()) <= 1:
yield n
a, b = b, a + b
def A258660_gen(): # generator of terms
for l in count(1):
if not isprime(l):
fs = divisors(l)
a, b = isqrt_rem(10 ** (l - 1))
if b > 0:
a += 1
for n in range(a, isqrt(10**l - 1) + 1):
n2 = n**2
ns = str(n2)
for g in fs:
y = 0
for h in range(0, l, g):
y += int(ns[h : h + g])
if not is_square(y):
break
else:
yield n2
def A350329(n):
a, b, c = 2**n, n * (n + 1), 2 ** (n + 1)
while (x := divmod(c - a, b))[1] != 0:
c *= 2
return x[0]
def A350576(n):
return n // (m := A055874(n)) - m
def A350509(n):
return n // A055874(n)
def A259629_gen(): # generator of terms
plist, p = [10, 15], 5
yield from plist
while True:
r = nextprime(p)
plist = [plist[-1] * 2 * r // p] + [d * r for d in plist]
p = r
yield from plist
def A259673(n):
return divisor_sigma(n, prime(n))
def A259836_gen(startvalue=0): # generator of terms
for n in count(max(startvalue, 0)):
m = n**3 + (n + 1) ** 3
for x in divisors(m):
x2 = x**2
if x2 > m:
break
if x != (2 * n + 1) and m < x * x2 and is_square(12 * m // x - 3 * x2):
yield n
break
def A259877_gen(): # generator of terms
yield 1
a = 1
for n in count(2):
a = 6 * a // (n - 1) if n % 2 else a * n * (n + 1) // 6
yield a
def A259981(n):
b, c = A002808(n), 0
for x in range(1, b):
for y in range(1, b):
if x != y:
w = b * (x - y)
for z in range(1, b):
if x != z:
if z * w == y * (x - z):
c += 1
return c
def A260224_gen():
return (
int("".join(x))
for n in count(1)
for x in product("135", repeat=n)
if is_prime(mpz("".join(x)))
)
def A260351(n): # assume 0 <= n <= 62
r, c = set(gmpy2digits(d, n) for d in range(n)), 0
dc = set(gmpy2digits(c, n))
while len(dc) < n - 1 or "0" in dc:
c += max(int(d, n) for d in r - dc)
dc = set(gmpy2digits(c, n))
return c
def A260374_gen(): # generator of terms
yield 0
g = 1
for i in count(1):
g *= i
s = isqrt(g)
t = g - s**2
yield int(t if t - s <= 0 else 2 * s + 1 - t)
def A261010(n):
return sum(int(d) for d in gmpy2digits(5**n, 3))
def A261182_gen():
return (
int("".join(d))
for l in count(1)
for d in product("279", repeat=l)
if isprime(int("".join(d)))
)
def A262963_helperf1(n):
s = gmpy2digits(n, 3)
m = len(s)
for i in range(m):
if s[i] == "0":
return int(s[:i] + "1" * (m - i), 3)
return n
def A262963_helperf2(n):
s = gmpy2digits(n, 4)
m = len(s)
for i in range(m):
if s[i] in ["0", "1"]:
return int(s[:i] + "2" * (m - i), 4)
return n
def A262963_gen(): # generator of terms
n = 1
while True:
m = A262963_helperf2(A262963_helperf1(n))
while m != n:
n, m = m, A262963_helperf2(A262963_helperf1(m))
yield m
n += 1
def A263133_gen(startvalue=0):
return (m for m in count(max(startvalue, 0)) if not ~(4 * m + 3) & m)
def A263299_gen():
return (
n
for n in (int("1" * k + str(k * (k + 1) + 1) + "1" * k) for k in count(0))
if isprime(n)
)
def A265433(n):
if n == 1:
return 0
if n == 3:
return 1
if (n % 3) == 0:
return 0
else:
pmaxlist = (
["3" * (n // 3) + "2"]
if (n % 3 == 2)
else ["3" * (n // 3 - 1) + "22", "3" * (n // 3 - 1) + "4"]
)
return sum(
1
for p in pmaxlist
for k in multiset_permutations(p)
if isprime(int("".join(k)))
)
def A267077(n):
if n == 0:
return 1
u, v, t, w = max(8, 2 * n), max(4, n) ** 2 - 9, 4 * n * (n + 1), n**2
while True:
m, r = divmod(v, t)
if not r and is_square(m * w + 1):
return m
v += u + 1
u += 2
def A267765_gen():
return (int(d, 5) for d in (str(i**2) for i in count(0)) if max(d) < "5")
def A267766_gen():
return (int(d, 6) for d in (str(i**2) for i in count(0)) if max(d) < "6")
def A267819_gen():
return (
int(d, 5)
for d in (str(i**2) for i in count(1))
if max(d) < "5" and isprime(int(d, 5))
)
def A267820_gen():
return (
int(d, 6)
for d in (str(i**2) for i in count(1))
if max(d) < "6" and isprime(int(d, 6))
)
def A268083_gen(): # generator of terms
b = 1
for n in count(1):
if len(factorint(n)) > 1 and gcd(b, n) == 1:
yield n
b = b * 2 * (2 * n + 1) // (n + 1)
def A268983_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not sum(
d * pow(int(divisor_sigma(d)), n // d, n) % n
for d in divisors(n, generator=True)
)
% n
)
def A269483(n):
return (
n
* (
n**2
* (n * (n**2 * (n**2 * (n * (n**2 * (n - 1) + 1) - 1) + 1) - 1) + 1)
- 1
)
+ 1
)
def A269483_gen(): # generator of terms
m = [
479001600,
-2674425600,
6386688000,
-8501915520,
6889478400,
-3482100720,
1080164160,
-194177280,
17948256,
-666714,
5418,
0,
1,
]
while True:
yield m[-1]
for i in range(12):
m[i + 1] += m[i]
def A270225_gen():
return (
p
for p in (prime(i) for i in count(2))
if p % 8 not in {5, 7} and isprime(p + 2)
)
def A270808_gen(): # generator of terms
a = 1
while True:
b = a // (max(primefactors(a) + [1])) + 1
yield b // 2
a += b
if sys.version_info >= (3, 10):
def A271499_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if n.bit_count().bit_count() != 1)
else:
def A271499_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if bin(bin(n).count("1")).count("1") != 1
)
def A272328(n):
m = totient(n)
return sum(1 for k in range(1, n + 1) if m == totient(n + k))
def A274093_gen():
return chain((0,), (i for n in count(1) for i in (-n if n % 2 else n,) * n))
def A274094_gen():
return chain((0,), (i for n in count(1) for i in (n if n % 2 else -n,) * n))
def A274213_gen(): # generator of terms
blist = [1, 2, 3]
yield from blist
while True:
blist.append(blist[-blist[-3]] + 3)
yield blist[-1]
def A275573_gen(): # generator of terms
q = 0
for i in count(1):
q += Fraction(int(str(i)[::-1]), 10 ** len(str(i)))
if q.denominator == 1:
yield q + i * (i + 1) // 2
def A276399(n):
a = factorial(n - 1)
return a // gcd(n ** (n - 1) - 1, a)
def A276400(n):
a = n ** (n - 1) - 1
return a // gcd(factorial(n - 1), a)
def A276689(n):
x = continued_fraction_periodic(0, 1, n)
return min(x[1]) if len(x) > 1 else 0
def A276919(n):
ndict = {}
for i in range(n):
i3 = pow(i, 3, n)
for j in range(i + 1):
j3 = pow(j, 3, n)
m = (i3 + j3) % n
if m in ndict:
if i == j:
ndict[m] += 1
else:
ndict[m] += 2
else:
if i == j:
ndict[m] = 1
else:
ndict[m] = 2
count = 0
for i in ndict:
j = (1 - i) % n
if j in ndict:
count += ndict[i] * ndict[j]
return count
def A276920(n):
ndict = {}
for i in range(n):
i3 = pow(i, 3, n)
for j in range(i + 1):
j3 = pow(j, 3, n)
m = (i3 + j3) % n
if m in ndict:
if i == j:
ndict[m] += 1
else:
ndict[m] += 2
else:
if i == j:
ndict[m] = 1
else:
ndict[m] = 2
count = 0
for i in ndict:
j = (-i) % n
if j in ndict:
count += ndict[i] * ndict[j]
return count
def A277285_gen():
return chain(
(1,),
(
j
for j in (i**2 for i in count(1))
if pow(2, j, int(divisor_count(j))) == 1
),
)
def A277685(n): # output differs from sequence at n=14 due to multiple spellings.
return ord(unidecode.unidecode(num2words(n, lang="pt")).lower()[0]) - 96
def A281363(n):
m, q = 1, 4 * n**2 - 1
p = pow(2, 2 * n, q)
r = p
while r != 1:
m += 1
r = (r * p) % q
return m
def A282384_gen(startvalue=1):
return (i for i in count(max(startvalue, 1)) if str(i + 1) in str(i**2))
def A286261_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if not is_cubefree_string(bin(n)[2:]))
def A286298(n):
if n <= 1:
return n
a, b = divmod(n, 2)
return A286298(a) + 1 + b + (-1) ** b * (a % 2)
def A286333_gen(): # generator of terms
for l in count(0):
for w in product("1379", repeat=l):
for d in "0123456789":
for t in "1379":
s = "".join(w) + d + t
n = int(s)
for i in range(l + 1):
if not isprime(int(s)):
break
s = s[1:] + s[0]
else:
if n > 10 and not isprime(int(s)):
yield n
def A286901(n):
m = prevprime(n)
return (m + n) * (n - m + 1) // 2
def A287550_gen(): # generator of terms
p = 2
q, r, s = p + 72, p + 144, p + 216
while True:
np = nextprime(p)
if (
np == q
and isprime(r)
and isprime(s)
and nextprime(q) == r
and nextprime(r) == s
):
yield p
p, q, r, s = np, np + 72, np + 144, np + 216
def A288184(n):
d = 1
while True:
s = continued_fraction_periodic(0, 1, d)[-1]
if isinstance(s, list) and len(s) == n:
return d
d += 2
def A288185(n):
d = 2
while True:
s = continued_fraction_periodic(0, 1, d)[-1]
if isinstance(s, list) and len(s) == n:
return d
d += 2
def A288939_gen(startvalue=0):
return (
n
for n in count(max(startvalue, 0))
if not isprime(n)
and isprime(n * (n * (n * (n * (n * (n + 1) + 1) + 1) + 1) + 1) + 1)
)
def A289660(n):
return (
0
if n == 1
else int("".join(map(lambda x: str(x[0]) * x[1], sorted(factorint(n).items()))))
- n
)
def A290126(n):
i = 1
while len(divisors(i)) < n or not isprime(sum(divisors(i)[-n:])):
i += 1
return i
def A290435_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if sum(factorint(n).values()) == len(factorint(n)) == 2
and isprime(1 + sum(factorint(n).keys()))
)
def A291460_gen(startvalue=1):
return (
2 * x
for x in count(max(startvalue // 2 + startvalue % 2, 1))
if str(int(bin(x).rstrip("0"), 2)) in str(2 * x)
)
def A292931_gen(startvalue=0):
return (
n for n in count(max(startvalue, 0)) if not sum(int(d) for d in str(3**n)) % 7
)
def A296012_gen(): # generator of terms
p = 2
while True:
k = (p - 2) // 3
if not (isprime(k) or isprime(k + 2)):
yield p
p = nextprime(p)
def A297574(n):
m = n + 1
mn = m * n
while pow(2, m, mn) != pow(2, n, mn):
m += 1
mn += n
return m
def A033307_gen():
return chain.from_iterable(sympydigits(m, 10)[1:] for m in count(1))
def A031076_gen():
return chain.from_iterable(sympydigits(m, 9)[1:] for m in count(1))
def A054634_gen():
return chain.from_iterable(sympydigits(m, 8)[1:] for m in count(0))
def A031035_gen():
return (d for m in count(1) for d in sympydigits(m, 8)[1:])
def A030998_gen():
return chain.from_iterable(sympydigits(m, 7)[1:] for m in count(0))
def A030548_gen():
return chain.from_iterable(sympydigits(m, 6)[1:] for m in count(1))
def A031219_gen():
return chain.from_iterable(sympydigits(m, 5)[1:] for m in count(1))
def A030373_gen():
return chain.from_iterable(sympydigits(m, 4)[1:] for m in count(1))
def A054635_gen():
return chain.from_iterable(sympydigits(m, 3)[1:] for m in count(0))
def A003137_gen():
return (d for m in count(1) for d in sympydigits(m, 3)[1:])
def A030190_gen():
return (int(d) for m in count(0) for d in bin(m)[2:])
def A298312_gen(): # generator of terms
n, m = 1, 30
while True:
k = prevprime(m // 3)
k2 = nextprime(k)
if prevprime(k) + k + k2 == m or k + k2 + nextprime(k2) == m:
yield n * (3 * n - 2)
n += 1
m += 18 * n + 3
def A298313_gen(): # generator of terms
n, m = 1, 30
while True:
k = prevprime(m // 3)
k2 = prevprime(k)
k3 = nextprime(k)
if k2 + k + k3 == m:
yield k2
elif k + k3 + nextprime(k3) == m:
yield k
n += 1
m += 18 * n + 3
@lru_cache(maxsize=None)
def A298356(n):
if n <= 2:
return 1
c, j = A298356(n - 1) + A298356(n - 2), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A298356(k1)
j, k1 = j2, n // j2
return c + n - j + 1
@lru_cache(maxsize=None)
def A298357(n):
if n <= 2:
return n + 1
c, j = A298357(n - 1) + A298357(n - 2), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A298357(k1)
j, k1 = j2, n // j2
return c + 2 * (n - j + 1)
@lru_cache(maxsize=None)
def A298369(n):
if n <= 2:
return 1
c, j = A298369(n - 1) + A298369(n - 2), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 * (j2 - 1) - j * (j - 1)) * A298369(k1) // 2
j, k1 = j2, n // j2
return c + (n * (n + 1) - j * (j - 1)) // 2
@lru_cache(maxsize=None)
def A298370(n):
if n <= 2:
return n + 1
c, j = A298370(n - 1) + A298370(n - 2), 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 * (j2 - 1) - j * (j - 1)) * A298370(k1) // 2
j, k1 = j2, n // j2
return c + 2 * (n * (n + 1) - j * (j - 1)) // 2
def A298827(n):
return n_order(3, 3**n + 2)
def A301631(n):
return (
Fraction(comb(2 * n, n)) / (n + 1) - Fraction(4**n) / (n + 1) ** 2
).numerator
def A301861(n):
return int(sum(mpz(d) for d in gmpy2digits(fac(fac(n)))))
def A301943(n):
return sum(1 for i in range(1, 10 ** (n - 1) + 1) if isprime(100 * i**2 + 1))
def A302021_gen(): # generator of terms
klist = [isprime(i**2 + 1) for i in range(6)]
for k in count(0):
i = isprime((k + 6) ** 2 + 1)
if klist[0] and klist[2] and i:
yield k
klist = klist[1:] + [i]
def A302087_gen(): # generator of terms
klist = [isprime(i**2 + 1) for i in range(6)]
for k in count(0):
i = isprime((k + 6) ** 2 + 1)
if klist[0] and i:
yield k
klist = klist[1:] + [i]
def A302294(n):
s = set()
for i in range(1, (n + 3) // 2):
for j in divisors(i):
for k in divisors(n - i):
if j != k:
s.add((min(j, k), max(j, k)))
return 3 * divisor_count(n) + 2 * len(s) - 1
def A302552(n):
return sum((6, 2, 5, 5, 4, 5, 6, 3, 7, 6)[int(d)] for d in str(prime(n)))
def A303108_gen(): # generator of terms
blist = [2, 5]
yield from blist
for n in count(3):
blist = [blist[1], 3 * (n - 1) * blist[-1] - (2 * n - 3) * (n - 2) * blist[-2]]
yield blist[-1]
def A303109_gen(): # generator of terms
blist = [0, 1]
yield from blist
for n in count(2):
blist = [
blist[1],
(3 * n * (n - 1) + 1) * blist[-1] - (2 * n - 3) * (n - 1) ** 3 * blist[-2],
]
yield blist[-1]
@lru_cache(maxsize=None)
def A304212_helper(n, i):
return (
1
if n == 0 or i == 1
else A304212_helper(n, i - 1) + A304212_helper(n - i, min(i, n - i))
)
def A304212(n):
return A304212_helper(n**3 - n**2, n**2)
def A305377(n):
m, tlist, s = prime(n), [1, 2, 4], 0
while tlist[-1] + tlist[-2] + tlist[-3] <= m:
tlist.append(tlist[-1] + tlist[-2] + tlist[-3])
for d in tlist[::-1]:
s *= 2
if d <= m:
s += 1
m -= d
return s
def A305380(n):
m, tlist, s = 2**n, [1, 2, 4], 0
while tlist[-1] + tlist[-2] + tlist[-3] <= m:
tlist.append(tlist[-1] + tlist[-2] + tlist[-3])
for d in tlist[::-1]:
s *= 2
if d <= m:
s += 1
m -= d
return s
def A305876(n):
m, tlist, s = 2**n, [1, 2], 0
while tlist[-1] + tlist[-2] <= m:
tlist.append(tlist[-1] + tlist[-2])
for d in tlist[::-1]:
s *= 2
if d <= m:
s += 1
m -= d
return s
def A306392(n):
return int(
"".join("1" if d == "2" else ("2" if d == "1" else d) for d in str(2**n))
)
def A306494(n):
k = n
for m in count(0):
s = str(k)
for i in range(1, len(s)):
if s[i] == s[i - 1]:
return m
k *= 3
def A307535(n):
r = 2**n
m, k = 2**r + 1, 0
w = m
while not isprime(w):
k += 1
w += r
return k
def A308395_gen(): # generator of terms
w = 0
for y in count(1):
w += y
z = 0
for x in range(1, y + 1):
z += x
if is_square(8 * (w + z) + 1):
yield y
break
def A318358_gen(): # generator of terms
yield 2
bset, p, q = {2}, 2, 4
while True:
r = sorted(
next(
zip(*diop_quadratic(symbolx**2 + q - p * symboly - symbolx * symboly))
)
)
for a in r[bisect.bisect_right(r, 0) :]:
if a not in bset:
yield a
bset.add(a)
break
p += a
q += a**2
def A320059(n):
c1, c2 = 1, 1
for p, a in factorint(n).items():
c1 *= (p ** (2 * a + 1) - 1) // (p - 1)
c2 *= (p ** (a + 1) - 1) // (p - 1)
return c1 - c2
def A320262(n):
return int(
"".join(
d + "0" for d in split("(0+)|(1+)", bin(n)[2:]) if d != "" and d != None
),
2,
)
def A320263(n):
return int(
"".join(
"0" + d for d in split("(0+)|(1+)", bin(n)[2:]) if d != "" and d != None
),
2,
)
def A320890_gen(): # generator of terms
b = 11
yield b
while True:
a0, a1, s = 0, 0, ""
for d in str(b):
if d == "0":
a0 += 1
s += bin(a0)[2:]
else:
a1 += 1
s += bin(a1)[2:]
b = int(s)
yield b
def A322183_gen():
return (int(str(d), 2) for d in A320890_gen())
def A321210_gen(): # generator of terms
for i in count(0):
s = bin(i)[2:]
s += s[-2::-1]
p = int(s) + int("02" * (len(s) // 2) + "0")
q = 6 * p + 1
t = str(q)
if t == t[::-1] and isprime(p) and isprime(q):
yield q
def A321443(n):
if n == 0:
return 1
c = 0
for i in range(n):
mi = i * (i + 1) + n
for j in range(i + 1, n + 1):
k = mi - j * j
if k < 0:
break
if not k % j:
c += 1
return c
def A321803(n):
return int(
"0"
+ "".join(
d if len(d) != 1 else ""
for d in split("(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)", str(n))
if d != "" and d != None
)
)
def A321804(n):
return (lambda x: int(x) if x != "" else -1)(
"".join(
d if len(d) != 1 else ""
for d in split("(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)", str(n))
if d != "" and d != None
)
)
def A322609_gen(startvalue=1):
return (
k
for k in count(max(startvalue, 1))
if sum(
d
for d in divisors(k, generator=True)
if max(factorint(d).values(), default=1) >= 2
)
== 2 * k
)
def A323192_gen(): # generator of terms
for k in count(0):
n = isqrt(2 ** (2 * k + 1))
if n * (n - 1) + 2 ** (len(bin(n)) - 2) - 2 ** (len(bin(n**2)) - 2) > 0:
yield n
def A328291(n):
if n > 9876543210 or n % 100 == 0:
return 0
k = 9876543210 // n
m = k * n
s = str(m)
while len(set(s)) != len(s):
k -= 1
m -= n
s = str(m)
return k
@lru_cache(maxsize=None)
def A328967(n):
if n == 0:
return 1
c, j = n - 1, 1
k1 = (n - 1) // j
while k1 > 1:
j2 = (n - 1) // k1 + 1
c += (j2 - j) * A328967(k1)
j, k1 = j2, (n - 1) // j2
return j - c
def A329792(n):
if n % 10:
m, s = 1, set("12345")
while not set(str(m * n)) <= s:
m += 1
return m
else:
return -1
def A329793(n):
if n % 10:
m, s = n, set("12345")
while not set(str(m)) <= s:
m += n
return m
else:
return -1
def A331759(n):
return (2 * n + 1) ** 2 + sum(
totient(i) * (2 * n + 2 - i) * (4 * n + 4 - i) for i in range(2, 2 * n + 2)
)
def A331760(n):
return (
n**2
+ sum(
totient(i) * (2 * n + 1 - i) * (4 * n + 2 - i) for i in range(2, 2 * n + 1)
)
// 4
)
def A333034(n):
return sum(int(d) for i in range(10 ** (n - 1), 10**n) for d in str(i**2))
def A333073(n):
f = 1
for i in range(1, n + 1):
f = lcm(f, i)
f = int(f)
glist = []
for i in range(1, n + 1):
glist.append(f // i)
m = 1 if n < 2 else primorial(n, nth=False) // primorial(n // 2, nth=False)
k = m
while True:
p, ki = 0, -k
for i in range(1, n + 1):
p = (p + ki * glist[i - 1]) % f
ki = (-k * ki) % f
if p == 0:
return k
k += m
def A333074(n):
f, g = int(factorial(n)), []
for i in range(n + 1):
g.append(int(f // factorial(i)))
m = 1 if n < 2 else prod(primefactors(n))
k = m
while True:
p, ki = 0, 1
for i in range(n + 1):
p = (p + ki * g[i]) % f
ki = (-k * ki) % f
if p == 0:
return k
k += m
def A333420_T(n, k): # T(n,k) for A333420
if k == 1:
return int(factorial(n))
if n == 1:
return k * (k + 1) // 2
if k % 2 == 0 or (k >= n - 1 and n % 2 == 1):
return (k * (k * n + 1) // 2) ** n
if k >= n - 1 and n % 2 == 0 and k % 2 == 1:
return ((k**2 * (k * n + 1) ** 2 - 1) // 4) ** (n // 2)
nk = n * k
nktuple = tuple(range(1, nk + 1))
nkset = set(nktuple)
count = 0
for firsttuple in combinations(nktuple, n):
nexttupleset = nkset - set(firsttuple)
for s in permutations(sorted(nexttupleset), nk - 2 * n):
llist = sorted(nexttupleset - set(s), reverse=True)
t = list(firsttuple)
for i in range(0, k - 2):
itn = i * n
for j in range(n):
t[j] += s[itn + j]
t.sort()
w = 1
for i in range(n):
w *= llist[i] + t[i]
if w > count:
count = w
return count
def A333446_T(n, k): # T(n,k) for A333446
c, l = 0, list(range(1, k * n + 1, k))
lt = list(l)
for i in range(n):
for j in range(1, k):
lt[i] *= l[i] + j
c += lt[i]
return c
def A333463(n):
return sum(
(2 * sum(d // k for k in range(1, isqrt(d) + 1)) - isqrt(d) ** 2)
* totient(n // d)
for d in divisors(n, generator=True)
)
def A333577(n):
if n == 2:
return 0
p = prime(n)
q, r = nextprime(p), 10 ** len(str(p))
return p * q * mod_inverse(q, r) % (q * r)
def A334841(n):
return 2 * bin(n)[-1:1:-2].count("1") - (len(bin(n)) - 1) // 2 if n > 0 else 0
def A335233_gen(): # generator of terms
f = 1
for k in count(1):
f *= k
g = 1
for i in range(1, k + 1):
g += f
if isprime(g):
break
else:
yield k
def A335402_gen():
return chain((0, 1, 2, 4), (prime(i) for i in count(3)))
def A336298(n):
return prevprime(prime(n) // 2 + 1)
def A337106(n):
return 0 if n <= 1 else divisor_count(factorial(n)) - 2
def A337174(n):
return (divisor_count(n) + 1) ** 2 // 4
def A337988_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
for d in divisors(n):
if 2 * d * d >= n:
break
a, b = integer_nthroot(n - d * d, 2)
if b and n % a == 0:
yield n
break
def A338577_gen(): # generator of terms
p, q, r = 2, 3, 5
while True:
if (q - p) * (r - p) > p:
yield p
p, q, r = q, r, nextprime(r)
def A339485(n):
c, primeset2 = n, set(prime(i) for i in range(1, n))
primeset = primeset2 | {prime(n)}
for l in range(2, n + 1):
for d in combinations(primeset, l):
a, b = divmod(sum(d), l)
if b == 0 and a in primeset2:
c += 1
return c
@lru_cache(maxsize=None)
def A339507(n):
pallist = set(i for i in range(1, n * (n + 1) // 2 + 1) if str(i) == str(i)[::-1])
return (
1
if n == 0
else A339507(n - 1)
+ sum(
sum(d) + n in pallist
for i in range(n)
for d in combinations(range(1, n), i)
)
)
def A339573(n):
return n * (n + 1) // 6 - 1
def A340667(n):
return 0 if n == 0 else int(bin(n)[2:].replace("0", "0" * n), 2)
def A340835(n):
if n == 0:
return 0
s = str(n)
for i, x in enumerate(s):
if x != "9":
break
else:
return n
s1, s2 = s[: i + 1], s[i + 1 :]
if s2 == "":
if s1[-1] == "0":
return int(str(n + 1)[::-1])
else:
return int(s[::-1])
if int(s2) <= 1:
return int("1" + s2[-2::-1] + s1[::-1])
else:
return int("1" + "0" * (len(s2) - 1) + str(int(s1) + 1)[::-1])
def A340836(n):
if n == 0:
return 0
s = bin(n)[2:]
i = s.find("0")
if i == -1:
return n
s1, s2 = s[: i + 1], s[i + 1 :]
if s2 == "":
return n + 1
if int(s2) <= 1:
return int("1" + s2[-2::-1] + s1[::-1], 2)
else:
return int("1" + "0" * (len(s2) - 1) + bin(int(s1, 2) + 1)[:1:-1], 2)
def A340868_gen(): # generator of terms
p, q, r, s = 2, 3, 5, 7
for k in count(1):
if pow(p, q, r) == s % r:
yield k
p, q, r, s = q, r, s, nextprime(s)
def A340967(n):
c, x = 0, n
while x > 1:
c += 1
x = n % sum(p * e for p, e in factorint(x).items())
return c
def A341280_gen(): # generator of terms
k2, d = 3, 2
for k in count(1):
if d % k == 0:
yield k
if isprime(k):
d -= k
if isprime(k2):
d += k2
k2 += 2
def A341718(n):
return int(str(2**n)[::-1]) - 1
def A341931(n):
k, m, r = n, n - 1, n if isprime(n) else -1
while m > 0:
k = int(str(k) + str(m))
if isprime(k):
r = m
m -= 1
return r
def A341934_gen(): # generator of terms
p, q, r, s = (
2,
3,
5,
7,
)
while True:
if isprime(2 * q * (p - r) + r * s):
yield p
p, q, r, s = q, r, s, nextprime(s)
def A342024(n):
f = factorint(n)
for p in f:
if primepi(p) < f[p]:
return 1
return 0
def A342040(n):
s = bin(n)[2:]
return int(s + s[-2::-1])
def A342131(n):
return (3 * n + 1) // 2 if n % 2 else n // 2 + n // 4
def A342280(n):
return 4 * n + 2 + isqrt(8 * n * (n + 1) + 2)
def A342281(n):
return isqrt(8 * n * (n + 1) + 2)
def A342288_gen(): # generator of terms
yield 2
b = 2
for n in count(1):
b = b * 4 * (2 * n - 1) * (2 * n + 3) // ((n + 1) * (n + 3))
yield b
def A342387_gen(): # generator of terms
yield 20
xlist, ylist, x, y = [4, 20, 39], [1, 6, 12], 39, 12
while True:
if len(str(x + 1)) == len(str(y + 1)) + 1:
yield x
x, y = 19 * xlist[-3] + 60 * ylist[-3] + 39, 6 * xlist[-3] + 19 * ylist[-3] + 12
xlist, ylist = xlist[1:] + [x], ylist[1:] + [y]
def A342388_gen(): # generator of terms
yield 6
xlist, ylist, x, y = [4, 20, 39], [1, 6, 12], 39, 12
while True:
if len(str(x + 1)) == len(str(y + 1)) + 1:
yield y
x, y = 19 * xlist[-3] + 60 * ylist[-3] + 39, 6 * xlist[-3] + 19 * ylist[-3] + 12
xlist, ylist = xlist[1:] + [x], ylist[1:] + [y]
def A342455(n):
return primorial(n) ** 5 if n >= 1 else 1
@lru_cache(maxsize=None)
def A342600(n, m=None): # A342600(n) = A342600(n,n)
if m == None:
m = n
return (
max(m, n)
if m < 2 or n < 2
else A342600(n - 1, m - 1) + A342600(n - 1, m - 2) + A342600(n - 2, m - 1)
)
def A342810_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if n == 1 or ((n % 9) + 1) * pow(10, n // 9, n) % n == 1
)
def A342956(n):
return (
sum(factorint(sum(p * e for p, e in factorint(n).items())).values())
if n > 1
else 0
)
def A343197_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if isprime(
sum(sum(p * e for p, e in factorint(i).items()) for i in range(2, n + 1))
)
)
@lru_cache(maxsize=None)
def A343511(n):
return 1 + sum(A343511(d) ** 2 for d in divisors(n) if d < n)
def A343524_gen(): # generator of terms
yield 0
for l in count(1):
for d in combinations("123456789", l):
s = "".join(d)
yield int(s + s[-2::-1])
for d in combinations("123456789", l):
s = "".join(d)
yield int(s + s[::-1])
def A343728_gen():
return (
n
for n in (2 * int(gmpy2digits(d, 5)) for d in count(0))
if set(str(n**2)[:-1]) <= set("13579")
)
def A343813(n):
p = prime(n)
pset = set(sieve.primerange(2, p + 1))
return sum(1 for d in partitions(p) if len(set(d) & pset) > 0)
def A343943(n):
fs = factorint(n)
return len(
set(sum(d) for d in multiset_combinations(fs, (sum(fs.values()) + 1) // 2))
)
def A343995(n):
plist = [p**q for p, q in factorint(2 * (2**n - 1)).items()]
return min(
k
for k in (crt(plist, d)[0] for d in product([0, -1], repeat=len(plist)))
if k > 0
)
def A343998(n):
fs = factorint(2 * n)
plist = [p ** fs[p] for p in fs]
return (
1
+ min(
k
for k in (crt(plist, d)[0] for d in product([0, -1], repeat=len(plist)))
if k > 0
)
) // 2
def A344057(n):
return 1 if n == 0 else 2 * n**2 * (2 * n - 1) * factorial(n - 1) ** 2
def A344983(n):
return int((mpz(2) ** 77232917 - 1) // mpz(10) ** (46498849 - n) % 10)
def A344984(n):
return int((mpz(2) ** 82589933 - 1) // mpz(10) ** (49724095 - n) % 10)
def A345421(n):
return igcdex(7, prime(n))[0]
def A345429(n):
return sum(
abs(u)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if w == 1
)
def A346120(n):
s, k, f = str(n), 0, 1
while s not in str(f):
k += 1
f *= k
return k
def A346527(n):
a, b, k, k2, m, r = -6 * (n + 1) ** 2, (n + 1) ** 4, 2, 4, 1, 0
while 2 * m + a < 0 or m * (m + a) + b < 0:
if isqrt(2 * m) - isqrt(m - 1) == n:
r = m
k += 1
k2 += 2 * k - 1
m = (k2 - 1) // 2
return r
def A346621(n):
return 0 if n <= 2 else A346621(n - 1) + (n if len(primefactors(n)) == 2 else 0)
def A346970(n):
c, ps = 2, primorial(n)
while True:
m = ps // gcd(ps, c)
if m == 1:
return c
p = max(primefactors(m))
for a in range(p, c, p):
if a * (c - a) % m == 0:
return c
c += 1
def A346971(n):
c, nlist = 1, list(range(1, n + 1))
while True:
mlist = [m for m in nlist if c % m]
if len(mlist) == 0:
return c
p = max(mlist)
for a in range(p, c, p):
for m in mlist:
if a % m and (c - a) % m:
break
else:
return c
c += 1
def A346988(n):
k, kn = n + 1, 1
while True:
if pow(n, kn, k) == 1:
return k
k += 1
kn += 1
def A347346(n):
if n % 10 == 0:
return 0
s = str(n)
if s == s[::-1]:
return n
for i in range(1, len(s)):
if s[:-i] == s[-i - 1 :: -1]:
return int(s[: -i - 1 : -1] + s)
def A347347(n):
if n % 2 == 0:
return 0
s = bin(n)[2:]
if s == s[::-1]:
return n
for i in range(1, len(s)):
if s[:-i] == s[-i - 1 :: -1]:
return int(s[: -i - 1 : -1] + s, 2)
def A347089(n):
return gcd(
divisor_count(n), sum(gcd(d, n // d) for d in divisors(n, generator=True))
)
def A348296(n):
c, k = 0, 0
while c != n:
k += 1
c += -1 if (isqrt(2 * k * k) - k) % 2 else 1
return k
def A348412_gen(startvalue=2):
return (
2 * n
for n in count(max(startvalue // 2 + startvalue % 2, 1))
if (lambda x, y: 2 * gcd(x, y * n) >= x)(divisor_sigma(n), divisor_sigma(n, 0))
)
def A000075(n):
return (
0
if n == 0
else len(
set(
2 * x**2 + 3 * y**2
for x in range(1 + isqrt(2 ** (n - 1)))
for y in range(1 + isqrt((2**n - 2 * x**2) // 3))
if 0 < 2 * x**2 + 3 * y**2 <= 2**n
)
)
)
def A008506_gen(): # generator of terms
m = [13, -65, 221, -494, 793, -923, 793, -494, 221, -65, 13, 0, 1]
while True:
yield m[-1]
for i in range(12):
m[i + 1] += m[i]
@lru_cache(maxsize=None)
def A015613(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * (A015613(k1) + k1) - 1)
j, k1 = j2, n // j2
return (n * (n - 3) - c + j) // 2
def A015942_gen(startvalue=2):
return (
n
for n in count(max(startvalue + startvalue % 2, 2), 2)
if pow(2, n, n) == n // 2 + 1
)
def A018166(n):
i, j = iroot_rem(18**n, 5)
return int(i) + int(32 * j >= 10 * i * (4 * i * (2 * i * (i + 1) + 1) + 1) + 1)
def A020418_gen():
return (
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and len(s) == 79
)
def A020430_gen():
return (
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and len(s) == 91
)
def A031557_gen():
return (
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and len(s) % 2 == 0 and s[len(s) // 2 - 1] == 59
)
def A031597_gen():
return (
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and len(s) % 2 == 0 and s[len(s) // 2 - 1] == 99
)
def A031702_gen():
return (
n
for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in count(1))
if isinstance(s, list) and min(s) == 24
)
def A031713_gen():
return (
n
for n, d in ((n, continued_fraction_periodic(0, 1, n)[-1]) for n in count(1))
if isinstance(d, list) and min(d) == 35
)
def A031775_gen():
return (
n
for n, d in ((n, continued_fraction_periodic(0, 1, n)[-1]) for n in count(1))
if isinstance(d, list) and min(d) == 97
)
def A031777_gen():
return (
n
for n, d in ((n, continued_fraction_periodic(0, 1, n)[-1]) for n in count(1))
if isinstance(d, list) and min(d) == 99
)
def A030082_gen(): # generator of terms
for i in count(1):
p = prime(i)
q = p**3
if set(str(p)) <= set(str(q)):
yield q
def A030087_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if set(str(n)) & set(str(n**3)) == set() and isprime(n)
)
def A031415_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
cf = continued_fraction_periodic(0, 1, n)
if (
len(cf) > 1
and len(cf[1]) > 1
and len(cf[1]) % 2
and cf[1][len(cf[1]) // 2] == 2
):
yield n
def A035523_gen(): # generator of terms
yield 1
l = 1
while True:
l += reversedigits(l, 3)
yield l
def A037967(n):
return comb(comb(2 * n, n) + 1, 2)
def A044460_gen(startvalue=0):
return (
n
for n in count(max(startvalue, 0))
if "02" in gmpy2digits(n, 5) and "02" not in gmpy2digits(n + 1, 5)
)
def A045541_gen(): # generator of terms
yield 2
l = 2
while True:
l = int("".join(d for d in str(l**2) if not d in set(str(l))))
yield l
def A046380_gen(): # generator of terms
for x in pal10_gen():
a = factorint(x)
if sum(list(a.values())) == 6 and all(map(is_pal, a.keys())):
yield x
def A045572(n):
return 2 * (n + (n + 1) // 4) - 1
def A348480(n):
if n == 1:
return 1
xn = 2 * (n + (n + 1) // 4) - 1
for l in count(xn - 1):
for d in multiset_permutations(["0"] * (l - xn + 1) + ["1"] * (xn - 1)):
s = "1" + "".join(d)
if gcd(int(s), int(s[::-1])) == xn:
return int(s, 2)
def A046705_gen():
return (
n
for n in (
(10 ** (2 * l + 1) - 1) // 9 + d * 10**l
for l in count(0)
for d in (1, 2, 4, 6)
)
if isprime(n)
)
def A051202_gen(): # generator of terms
a2, a1 = 1, 1
for n in count(3):
a = abs(a1 + 2 * a2 - n)
if a == 0:
yield n
a1, a2 = a, a1
def A053964_gen(): # generator of terms
for l in count(1):
for p in product(*["479"] * l):
a, b = integer_nthroot(int("".join(p)), 2)
if b:
yield a
def A053965_gen(): # generator of terms
for l in count(1):
for p in product(*["479"] * l):
n = int("".join(p))
if is_square(n):
yield n
def A054793(n):
a, b = integer_nthroot(n, 4)
return (
n
if n <= 1
else A054793(a) ** 4
if b
else n + 1
if (n - a**4) % 2
else (n - 1) ** 4
)
def A059402_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if n % 10
and len(factorint(n)) > 1
and all(str(a**b) in str(n) for a, b in factorint(n).items())
)
def A061051(n):
if n == 0:
return 0
nstart = 10 ** (n - 1)
nend = 10 * nstart
for i in range(nstart, nend):
k = int(str(i) * 2)
if is_square(k):
return k
for i in range(nstart, nend):
si = str(i) * 2
for sj in "014569":
k = int(si + sj)
if is_square(k):
return k
def A062935_gen(): # generator of terms
n = 1
for i in count(1):
n *= i
s = str(n + 1)
if s == s[::-1]:
yield n + 1
def A065899(n):
return compositepi(factorial(composite(n)) // primorial(primepi(composite(n))))
def A066467_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if antidivisor_count(n) == 2)
def A066469_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if antidivisor_count(n) == 4)
def A066472_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if antidivisor_count(n) == 6)
def A073954_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if antidivisor_sigma(n) > 2 * n)
def A074713_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if antidivisor_sigma(n) == totient(n))
def A074730_gen():
return (n for n in (i**2 for i in count(1)) if is_square(antidivisor_sigma(n)))
def A076642(n):
y = Poly(rf(6 * symbolx + 1, n)).all_coeffs()[::-1]
return y.index(max(y))
def A350595(n):
return sum(
(-1 if (n + k) % 2 else 1) * comb(2 * n, k) ** n for k in range(2 * n + 1)
)
def A082439_gen(): # generator of terms
yield 3
for i in count(1):
s = str(i)
n = int(s + "3" + s[::-1])
if isprime(n):
yield n
def A082617_gen(): # generator of terms
yield 1
a = 1
while True:
p = 2
b = p * a
bs = str(b)
while bs != bs[::-1] or max(factorint(b).values()) > 1:
p = nextprime(p)
b = p * a
bs = str(b)
yield b
a = b
def A082646_gen(): # generator of terms
for i in count(1):
p = str(prime(i))
h = [p.count(d) for d in "0123456789" if d in p]
if min(h) == max(h):
yield int(p)
def A085375_gen(): # generator of terms
b = 1
for n in count(0):
yield b
b = b * 2 * (n + 5) * (2 * n + 3) // ((n + 1) * (n + 2))
def A090850_gen(): # generator of terms
yield 0
f, blist = 6, [0]
while True:
blist = [blist[0] + f] + list(map(add, blist[:-1], blist[1:])) + [1]
yield from blist
def A096217_gen(): # generator of terms
yield 1
blist = [1]
for n in count(2):
b = sum(x for x in blist if gcd(x, n) == 1)
blist.append(b)
yield b
def A096488(n):
return len(set(continued_fraction(sqrt((10**n - 1) // 9))[-1]))
def A097963_gen():
return chain(
(1,),
accumulate(
repeat(15),
lambda x, _: x
+ 2
+ len(num2words(x, to="ordinal").replace(" and ", " ").replace(", ", " ")),
),
)
def A101701_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if n == sum(int(d) for d in (str(x)[::-1] for x in divisors(n)))
)
def A104476(n):
return comb(n + 7, 7) * comb(n + 11, 7)
def A104476_gen(): # generator of terms
m = [3432, -1716, 660, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330, 330]
while True:
yield m[-1]
for i in range(14):
m[i + 1] += m[i]
def A105252(n):
return comb(n + 5, n) * comb(n + 9, n)
def A105252_gen(): # generator of terms
m = [2002, -4433, 3487, -1133, 127, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
while True:
yield m[-1]
for i in range(14):
m[i + 1] += m[i]
def A105253(n):
return comb(n + 6, n) * comb(n + 10, n)
def A105253_gen(): # generator of terms
m = [8008, -22022, 23023, -11297, 2563, -209] + [1] * 11
while True:
yield m[-1]
for i in range(16):
m[i + 1] += m[i]
def A105943(n):
return comb(n + 7, n) * comb(n + 10, 7)
def A105943_gen(): # generator of terms
m = [3432, -3432, 1320, 0] + [120] * 11
while True:
yield m[-1]
for i in range(14):
m[i + 1] += m[i]
def A107337_gen(): # generator of terms
yield 1
blist, c = [1], 1
while True:
blist = list(
chain.from_iterable(
(
[1, 2, 1, 3, 2, 3, 1] if d == 1 else [3] if d == 2 else [1]
for d in blist
)
)
)
yield from blist[c:]
c = len(blist)
def A107908_gen(): # generator of terms
m = [21, -13, 3] + [1] * 5
yield m[-1]
while True:
for i in range(7):
m[i + 1] += m[i]
yield m[-1]
def A108646_gen(): # generator of terms
m = [77, -85, 28, -1, 1, 1, 1, 1]
while True:
yield m[-1]
for i in range(7):
m[i + 1] += m[i]
def A109351_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if integer_nthroot(sum(antidivisors(n)), 3)[1]
)
def A110690_gen(): # generator of terms
m = [62, -65, 20, 0, 1, 1, 1, 1, 1]
while True:
yield m[-1]
for i in range(8):
m[i + 1] += m[i]
def A110693_gen(): # generator of terms
m = [450, -816, 508, -121, 10, 1, 1, 1, 1, 1]
while True:
yield m[-1]
for i in range(9):
m[i + 1] += m[i]
def A113009(n):
return sum(int(d) for d in str(n)) ** len(str(n))
def A113010(n):
return len(str(n)) ** sum(int(d) for d in str(n))
def A115286_gen(): # generator of terms
m = [120, -300, 272, -96, 8, 0, 0]
while True:
yield m[-1]
for i in range(6):
m[i + 1] += m[i]
def A116054_gen(): # generator of terms
k, m = 1, 2
for n in count(0):
for i in range(k, m):
s = str(i * n)
if s == s[::-1]:
yield i
k, m = m, nextprime(m)
def A117790_gen(): # generator of terms
yield 1
a, b = 1, 3
while True:
if isprime(sum(int(d) for d in str(b))):
yield b
a, b = b, a + b
def A118548_gen():
return (
n
for n in (x**2 for x in count(1))
if not (str(n).count("0") or n % prod(int(d) for d in str(n)))
)
def A118575_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if (m := A031347(n))
and not (
str(n).count("0")
or n % ((1 + (n - 1) % 9))
or n % m
or n % sum(int(d) for d in str(n))
or n % prod(int(d) for d in str(n))
)
)
def A350578_gen(): # generator of terms
yield 0
b, bcounter = 0, Counter({0})
for n in count(1):
b += -n if b - n >= 0 and bcounter[b - n] <= bcounter[b + n] else n
bcounter[b] += 1
yield b
def A350579(n):
b, bcounter = 0, Counter({0})
for m in count(1):
if bcounter[b] == n:
return b
b += -m if b - m >= 0 and bcounter[b - m] <= bcounter[b + m] else m
bcounter[b] += 1
def A122004_gen(): # generator of terms
p = 2
while True:
if (
0
== sum(pow(prime(i), prime(j), p) for i in range(1, p) for j in range(1, p))
% p
):
yield p
p = nextprime(p)
def A123373(n):
return sum(prime(i) ** prime(j) for i in range(1, n + 1) for j in range(1, n + 1))
def A086787(n):
return (
1
- digamma(n)
- EulerGamma
+ sum(Fraction(i ** (n + 1), i - 1) for i in range(2, n + 1))
)
def A128287_gen(): # generator of terms
yield 1
x, s = 1, 2
for i in count(2):
x = x * (4 * i - 2) // (i + 1)
s += x
if not (isprime(i) or s % i):
yield i
def A130870_gen(): # generator of terms
for i in pal10_odd_range_gen():
if (
i > 2
and isprime(i)
and max(factorint(i - 1).values()) > 1
and max(factorint(i + 1).values()) > 1
):
yield i
def A132365(n):
a, b, m, s = 2, 1, 0, str(n)
while True:
if s in str(a):
return m
m += 1
a, b = b, a + b
def A134009_gen(): # generator of terms
yield 1
b = 1
while True:
i, j = isqrt_rem(3 * b**2)
b = i + int(4 * (j - i) >= 1)
yield int(b)
def A135923_gen(): # generator of terms
m = [1680, -840, -1380, -240, 641, 393, -209, -10, 0]
yield m[-1]
while True:
for i in range(8):
m[i + 1] += m[i]
yield m[-1]
def A137079_gen():
return (
int("".join(a) + b)
for l in count(0)
for a in product("2356", repeat=l)
for b in ("5", "6")
if set(str(int("".join(a) + b) ** 2)) <= {"2", "3", "5", "6"}
)
def A137093_gen():
return (
int("".join(a))
for l in range(1, 10)
for a in product("2456", repeat=l)
if set(str(int("".join(a)) ** 2)) <= {"2", "4", "5", "6"}
)
def A138584_gen(): # generator of terms
for l in count(0):
for d in product("35", repeat=l):
s = "".join(d)
n = int(s + "3" + s[::-1])
if isprime(n):
yield n
n += 2 * 10**l
if isprime(n):
yield n
@lru_cache(maxsize=None)
def A140466(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (A140466(k1) // 2 - 1)
j, k1 = j2, n // j2
return 2 * (n * (n - 1) - c + j)
def A145203_gen():
return (
primepi(3 * n * (n + 1) + 1) for n in count(0) if isprime(3 * n * (n + 1) + 1)
)
def A145285(n):
return (5, 8, 12, 16, 20, 25, 28, 32)[n - 1] if n <= 8 else 4 * n + 1
def A147773(n):
i, j = iroot_rem(n**n, 3)
return int(i + int(8 * j >= 6 * i * (2 * i + 1) + 1))
def A158215(n):
if n == 1:
return 11
if n == 2:
return 0
p2 = prime(n) // 2
l = p2
while True:
for i in combinations(range(l), l - p2):
s = ["1"] * l
for x in i:
s[x] = "0"
s = "".join(s)
q = int(s + "1" + s[::-1])
if isprime(q):
return q
l += 1
def A153568(n):
a, b, = (
0,
1,
)
for _ in range(n):
a, b = b, a + b
return (lambda m: 2 * sum(a // k for k in range(1, m + 1)) - m * m)(isqrt(a))
def A158962(n):
m = 1
while True:
for i in range(n):
if not isprime(int(str(m) * (i + 1)) - 1):
break
else:
return m
m += 1
def A160828_gen(): # generator of terms
m = [96, 0, 80, 80, 98]
while True:
yield m[-1]
for i in range(4):
m[i + 1] += m[i]
def A160943(n):
return n + sum(int(d) for d in str(n - 1)) + sum(int(d) for d in str(n + 1))
def A161354_gen():
return (m for m in (n**3 for n in count(1)) if isprime(int(str(m)[::-1])))
@lru_cache(maxsize=None)
def A162459(n):
if n == 0:
return 0
c, j = n, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A162459(k1) // 2 ** (k1 - 1)
j, k1 = j2, n // j2
return 2 ** (n - 1) * (j - c)
def A167218_gen(): # generator of terms
for l in count(1):
plist = []
l1, l2 = 10 ** (l - 1), 10**l
m = isqrt(l1)
if m**2 + 1 < l1:
m += 1
while (k := m**2 + 1) < l2:
if k % 10:
p = int(str(k)[::-1])
if isprime(p):
plist.append(p)
m += 1
yield from sorted(plist)
def A167807_gen(): # generator of terms
for i in count(3):
n = i * (i + 1) * (2 * i + 1) // 6
p2 = prevprime(n // 3)
p1, p3 = prevprime(p2), nextprime(p2)
q = p1 + p2 + p3
while q <= n:
if q == n:
yield n
p1, p2, p3 = p2, p3, nextprime(p3)
q = p1 + p2 + p3
def A171642_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
d = divisors(n)
s = sum(d)
if s % 2 and 2 * n <= s and s == 3 * sum(x for x in d if x % 2):
yield n
def A173102(n):
return (9 * n**2 - (n % 2)) // 4
def A173208_gen(): # generator of terms
yield 2
a, b = 2, 3
while True:
if (
max(factorint(b).values()) <= 1
and max(factorint(b - 1).values()) <= 1
and max(factorint(b + 1).values()) <= 1
):
yield b
a, b = b, a + b
@lru_cache(maxsize=None)
def A175549(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * A175549(k1)
j, k1 = j2, n // j2
return 4 * n * (n - 1) * (2 * n + 5) - c + 26 * (j - 1)
def A175583_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
d = divisors(n)
s = sum(d)
if not s % 2 and max(d) <= s // 2 and isprime(s // 2 - n):
for x in range(1, 2 ** len(d)):
if sum(Subset.unrank_binary(x, d).subset) == s // 2:
yield n
break
def A182578(n):
m, tlist, s = n**n, [1, 2], 0
while tlist[-1] + tlist[-2] <= m:
tlist.append(tlist[-1] + tlist[-2])
for d in tlist[::-1]:
if d <= m:
s += 1
m -= d
return s
def A185173(n):
c = n * (n + 1) // 2
for i in range(2, n + 1):
for j in range(i + 1, n + 1):
pset = set(range(2, n + 1)) - {i, j}
for p in permutations(pset):
q, rset, rl = [j, 1, i] + list(p), set(), 0
for k in range(n):
r = 0
for l in range(n):
r += q[(k + l) % n]
if r not in rset:
rset.add(r)
rl += 1
if rl >= c:
break
else:
continue
break
else:
c = rl
return c
def A185267(n):
p = prime(n)
s = str(p)
if s == s[::-1]:
return p
for i in range(1, len(s)):
if s[i:] == s[-1 : i - 1 : -1]:
return int(s + s[i - 1 :: -1])
def A185695(n):
p, k, m = 2, 61**n, 10
q, m2 = p % k, m % k
while True:
p = nextprime(p)
while p >= m:
m *= 10
m2 = m % k
q = (q * m2 + p) % k
if q == 0:
return p
def A185698(n):
p, k, m = 2, 67**n, 10
q, m2 = p % k, m % k
while True:
p = nextprime(p)
while p >= m:
m *= 10
m2 = m % k
q = (q * m2 + p) % k
if q == 0:
return p
def A187975_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isqrt(2 * (n + 5) ** 2) - isqrt(2 * n**2) == 8
)
def A188089_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isqrt(3 * (n + 4) ** 2) - isqrt(3 * n**2) == 6
)
def A188290_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isqrt(5 * (n + 4) ** 2) - isqrt(5 * n**2) == 8
)
def A192272_gen(startvalue=3): # generator of terms
for n in count(max(startvalue, 3)):
if (n * antidivisor_count(n)) % sum(antidivisors(n, generator=True)) == 0:
yield n
def A192276_gen(startvalue=3):
return (
n
for n in count(max(startvalue, 3))
if not n % sum(1 for d in range(2, n) if n % d and 2 * n % d in (d - 1, 0, 1))
)
def A192892(n):
return (
1
if n == 0
else sum(
1
for m in product([0, 1], repeat=n**2)
if (lambda x: x.det() == x.per())(Matrix(n, n, m))
)
)
def A194112(n):
return sum(isqrt(8 * j**2) for j in range(1, n + 1))
def A194116(n):
return sum(isqrt(13 * j**2) for j in range(1, n + 1))
def A194137(n):
return sum(isqrt(6 * j**2) for j in range(1, n + 1))
def A194140(n):
return n * (n + 1) // 2 + sum(isqrt(3 * j**2) for j in range(1, n + 1))
def A195349_gen(): # generator of terms
s, p = 0, 1
for k in count(1):
d = divisor_count(k)
s += d
p *= d
if p % s == 0:
yield k
def A197194_gen(): # generator of terms
m, k = [1] * 10, 1
while True:
yield k * m[-1]
k *= 9
for i in range(9):
m[i + 1] += m[i]
def A198193(n):
return sum((n - i) * int(j) for i, j in enumerate(bin(n)[2:]))
def A201009_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if primefactors(n)
== primefactors(
sum(int(n * e / p) for p, e in factorint(n).items()) if n > 1 else 0
)
)
def A205770(n):
m = 100**n
i = integer_nthroot(m, 5)[0]
return i + int(32 * m >= (1 + 2 * i) ** 5)
def A038103_gen():
return (
int(s)
for s in (gmpy2digits(n, 3) for n in count(0))
if s in gmpy2digits(int(s), 3)
)
def A350573_gen():
return (n for n in count(0) if (s := gmpy2digits(n, 3)) in gmpy2digits(int(s), 3))
def A214332_gen(): # generator of terms
yield 0
blist, c = [0], 1
while True:
blist = list(
chain.from_iterable(
([0, 1] if d == 0 else [2, 0, 2] if d == 1 else [] for d in blist)
)
)
yield from blist[c:]
c = len(blist)
def A216395(n):
if n == 1:
return 1
c = 0
for i in range(2 ** (n - 1) + 1, 2**n):
s1, s2 = sorted(str(i)), sorted(str(divisor_sigma(i)))
if len(s1) == len(s2) and s1 == s2:
c += 1
return c
def A216396(n):
c = 0
for i in range(2 ** (n - 1) + 1, 2**n):
s1, s2 = sorted(str(i)), sorted(str(divisor_sigma(i) - i))
if len(s1) == len(s2) and s1 == s2:
c += 1
return c
def A216873_gen(): # generator of terms
n = 1
for i in count(0):
s = str(n)
if sum(isprime(s.count(d)) for d in "0123456789") >= 9:
yield i
n *= 2
def A217186(n):
l, x = [str(d) * n for d in range(10)], 1
for m in count(0):
s = str(x)
for k in l:
if k in s:
return len(s)
x *= 3
def A217191(n):
if n == 1:
return 1
else:
l, y, x = [str(d) * n for d in range(10)], 0, 1
for m in count(1):
s = str(x)
for k in l:
if k in s:
return len(s)
y, x = x, y + x
def A217192(n):
if n == 1:
return 1
else:
l, y, x = [str(d) * n for d in range(10)], 2, 1
for m in count(1):
s = str(x)
for k in l:
if k in s:
return len(s)
y, x = x, y + x
def A349576_gen(): # generator of terms
blist = [1, 5]
yield from blist
while True:
blist = [blist[1], sum(blist) // gcd(*blist) + 1]
yield blist[-1]
def A225864_gen(): # generator of terms
for l in count(1):
plist, q = [p for p in [2, 3, 5, 7] if isprime(l - 1 + p)], (10**l - 1) // 9
for i in range(l):
for p in plist:
r = q + (p - 1) * 10**i
if not isprime(r):
yield r
def A226019_gen(): # generator of terms
yield 2
for l in count(1):
plist = []
l1, l2 = 10 ** (l - 1), 10**l
m = isqrt(l1)
if m**2 < l1:
m += 1
while (k := m**2) < l2:
if k % 2:
p = int(bin(k)[-1:1:-1], 2)
if isprime(p):
plist.append(p)
m += 1
yield from sorted(plist)
def A228000(n):
return min(factorint(144396166620968 * n + 1))
def A228295(n):
return 0 if n == 0 else 1 + integer_nthroot(12 * n**4, 4)[0]
def A235164_helper(n, b):
if n == 1:
t = list(range(1, b))
for i in range(1, b):
u = list(t)
u.remove(i)
yield i, u
else:
for d, v in A235164_helper(n - 1, b):
for g in v:
k = d * b + g
if not k % n:
u = list(v)
u.remove(g)
yield k, u
def A235164_gen():
return (a for n in count(2, 2) for a, b in A235164_helper(n - 1, n))
def A239437(n): # requires 3 <= n <= 62
m = n
while True:
s = "".join(gmpy2digits(i, m) for i in range(m))
for d in permutations(s, m):
if d[0] != "0":
c = mpz("".join(d), m)
for b in range(3, n):
if len(set(gmpy2digits(c, b))) == b:
break
else:
return int(c)
m += 1
def A239638_gen(): # generator of terms
p = 5
while True:
if (p % 6) == 5:
n = (p - 1) // 2
if pow(2, n, p) == 1 and isprime((2**n - 1) // p):
yield n
p = nextprime(p)
def A239942(n):
return factorial(prime(n)) - factorial(prime(n - 1))
def A240975(n):
return len(primefactors(n**3 - 1))
def A242028_gen():
return filter(lambda n: lcm(*antidivisors(n)) < n, count(3))
def A242092_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if primefactors(n) == primefactors(int(str(prime(n))[::-1]))
)
def A242347_gen():
yield 1
l = 2
while True:
l = int(bin(l)[2:])
yield len(str(l))
def A242930_gen():
return filter(
isprime, (a for a, b in (divmod(k**2 + 7, 11) for k in count(1)) if b == 0)
)
def A243097_gen(): # generator of terms
for n in count(1):
if n % 10:
s1 = str(n)
s2 = s1[::-1]
if s1 != s2 and not n % int(s2):
yield sum(int(d) for d in s1)
def A243112_gen(): # generator of terms
yield 0
a = 0
for n in count(1):
s = bin(n)[2:]
b = sum(s[i:].count("0") for i, d in enumerate(s, start=1) if d == "1")
if b > a:
yield n
a = b
def A243298_gen(): # generator of terms
m = [362880, -1491840, 2464560, -2082240, 945000, -220248, 22560, -680, 1, -1]
for n in count(1):
for i in range(9):
m[i + 1] += m[i]
if isprime(m[-1]):
yield n
def A244444_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if len(set(str(n + sum(divisors(n))))) == 1
and str(n + sum(divisors(n)))[0] == "1"
)
def A245048_gen():
return filter(lambda p: isprime(p**2 + 28), (prime(n) for n in count(1)))
def A245061_gen():
return (p for n, p in enumerate(prime(n) for n in count(1)) if is_square(p - n - 1))
def A245199_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if is_square(int(divisor_count(n))) and is_square(int(totient(n)))
)
def A245202_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if is_square(int(divisor_count(n) + totient(n)))
)
def A245270(n):
return int("".join(bin(y)[2:] for x in sorted(factorint(n).items()) for y in x), 2)
def A246666_gen(startvalue=1):
return (
n for n in count(max(startvalue, 1)) if isprime(3 * n * (n * (n + 4) + 10) + 28)
)
def A246757(n):
for i in range(10**n - 1, int("1" * n) - 1, -1):
pd = prod(int(d) for d in str(i))
if pd and not i % pd:
return i
def A246763_gen():
yield 1
c = 1
for n in count(2):
c = c * (4 * n - 2) // (n + 1)
yield c**2 % prime(n)
def A247000(n):
maxcount = 0
for i in range(2 ** (n - 1), 2**n):
s = format(i, "0" + str(n) + "b")
s, plist = s + s[:-1], []
for j in range(n):
for k in range(n):
t = s[j : j + k + 1]
if t == t[::-1] and not t in plist:
plist.append(t)
if len(plist) > maxcount:
maxcount = len(plist)
return maxcount
def A247048_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
if not (isprime(n) or isprime(n + 2)):
m = sum(p * e for p, e in factorint(n).items())
if isprime(m):
m2 = sum(p * e for p, e in factorint(n + 2).items())
if ((m2 == m + 2) or (m == m2 + 2)) and isprime(m2):
yield n
def A247108_gen(): # generator of terms
yield 1
blist = [1]
while True:
blist = list(accumulate([-blist[-1]] + blist))
yield from blist
def A247213_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if n <= 1 or not prod((p + 2) ** e for p, e in factorint(n).items()) % n
)
def A247592_gen(): # generator of terms
blist, m, c = [2], 2, 2
for n in count(1):
m += 2 * n + 1
if is_prime(m):
if is_square(m % blist[-1]):
yield c
blist.append(m)
c += 1
def A247650_gen(): # generator of terms
yield 1
blist, g, f = (
[1],
1,
(
(1 / symbolx**2 + 1 / symbolx + 1 + symbolx + symbolx**2)
* (1 / symboly**2 + 1 / symboly + 1 + symboly + symboly**2)
).expand(modulus=2),
)
for n in count(1):
s = [int(d, 2) for d in bin(n)[2:].split("00") if d != ""]
g = (g * f).expand(modulus=2)
if len(s) == 1:
blist.append(g.subs([(symbolx, 1), (symboly, 1)]))
else:
blist.append(prod(blist[d] for d in s))
yield blist[-1]
def A248587_gen(): # generator of terms
for i in count(3):
n = i**3
p3 = prevprime(n // 4)
p2, p4 = prevprime(p3), nextprime(p3)
p1 = prevprime(p2)
q = p1 + p2 + p3 + p4
while q <= n:
if q == n:
yield p1
p1, p2, p3, p4 = p2, p3, p4, nextprime(p4)
q = p1 + p2 + p3 + p4
def A248705_gen(): # generator of terms
x, m = 0, [6, -6, 1, 0]
while True:
for i in range(3):
m[i + 1] += m[i]
xn = prod(int(d) for d in str(m[-1]))
if xn > x:
x = xn
yield m[-1]
def A249586_gen(): # generator of terms
yield 0
m = [
119750400,
-658627200,
1546776000,
-2020606560,
1602266400,
-789354720,
237304980,
-40965390,
3576156,
-120849,
784,
0,
0,
]
while True:
for i in range(12):
m[i + 1] += m[i]
yield m[-1]
def A350037(n):
return pow(n, 2, (m := isqrt(n)) + int(4 * n >= (2 * m + 1) ** 2))
def A350046_gen(): # generator of terms
f = Counter()
for m in count(2):
f += Counter(factorint(m))
e = sorted(f.items())
if all(
d <= 1 or isprime(d)
for d in (abs(e[i + 1][1] - e[i][1]) for i in range(len(e) - 1))
):
yield m
def A249610_gen(): # generator of terms
m = [48, -56, 13, 1]
while True:
for i in range(3):
m[i + 1] += m[i]
if isprime(m[-1]):
yield m[-1]
def A249627(n):
return min(fs := factorint((10**n - 1) // 9)) * max(fs)
def A249875_gen(): # generator of terms
x = 1
while True:
yield 2 * sum(divmod(isqrt(2 * x), 2)) ** 2 + x
x *= 4
def A251853_gen():
(
int("".join(d))
for d in product("02468", repeat=4)
if not sum(int(y) for y in str(sum(int(x) for x in d))) % 2
)
def A253295_gen(): # generator of terms
yield 8
b = 8
while True:
b = int("".join((str(e) + str(p) for p, e in sorted(factorint(b).items()))))
yield b
def A253549(n):
p = prime(n)
for b in range(2, 17):
x, y, z = p, 0, 1
while x >= b:
x, r = divmod(x, b)
y += r * z
z *= 16
y += x * z
if isprime(y):
return y
def A253575_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if set(str(n)) & set(str(n**6)) == set() and isprime(n)
)
def A253578_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if set(str(n)) & set(str(n**10)) == set() and isprime(n)
)
def A253671_gen(): # generator of terms
yield 1
blist, l1, l2 = (0, 1), 1, 1
while True:
l2, l1 = l1, (blist := tuple(accumulate(reversed(blist), initial=0)))[-1]
yield l1 // l2
def A253769(n):
return (lambda m, p: 2 * sum(p // k for k in range(1, m + 1)) - m * m)(
isqrt(prime(n)), prime(n)
)
def A253912_gen():
return (n for n in (i**4 for i in range(10**6)) if isprime(int(str(n)[::-1])))
def A254058(n):
b, a1, a2, t = 1, 0, n, 2**n
while b < t:
a2 += 1
a1 += 1
b = (b * a2) // a1
return a2
def A254625_gen(): # generator of terms
c0, c1, c2 = 1, 8, 27
for n in count(1):
if max(c0, c1, c2) < n:
yield n
c0, c1, c2 = c1, c2, A007913(n + 3) ** 3
def A254648_gen(startvalue=10): # generator of terms
for n in count(max(startvalue, 10)):
m = str(n**2)
for a in combinations(range(1, len(m)), 2):
x, y, z = int(m[: a[0]]), int(m[a[0] : a[1]]), int(m[a[1] :])
if y != 0 and z != 0 and x + y + z == n:
yield n
break
def A254746_gen(): # generator of terms
yield 1
c, s, s2 = {}, 2, 4
for n in count(2):
for p, e in factorint(4 * n - 2).items():
if p in c:
c[p] += e
else:
c[p] = e
for p, e in factorint(n + 1).items():
if c[p] == e:
del c[p]
else:
c[p] -= e
if n == s2:
d, ps = 1, prime(s)
for p, e in c.items():
d = (d * pow(p, e, ps)) % ps
yield d
s2 += 2 * s + 1
s += 1
def A254999_gen():
return (
n
for n, m in (
(4 * k + 2, divisor_sigma_mod(4 * k + 2, 4 * k + 2)) for k in count(0)
)
if m and not n % m
)
def A255400(n):
f, i, s = 1, 0, re.compile("[0-9]*[1-9]0{" + str(n) + "}[1-9][0-9]*")
while s.match(str(f) + "1") is None:
i += 1
f *= i
return i
def A255911_gen(): # generator of terms
blist, c, m = [], 0, 0
for i in count(1):
d = divisor_count(i)
if d > m:
m = d
blist.append(i)
for j in range(c - 1, -1, -1):
q, r = divmod(i, blist[j])
if not r:
yield q
break
c += 1
def A256370_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if is_prime(5 * n * (n * (n * (n + 8) + 36) + 80) + 354)
)
def A256969_gen(): # generator of terms
c, bn, bd = 0, 1, 1
for k in count(1):
p = prime(k)
bn *= p
bd *= p - 1
while bn > c * bd:
yield k
c += 1
def A256985(n):
ilist, k = [1] * (n + 1), 1
jlist = [d % 10 for d in accumulate(ilist)]
jlist = [jlist[-1]] + jlist[:-1]
while ilist != jlist:
k += 1
jlist = [d % 10 for d in accumulate(jlist)]
jlist = [jlist[-1]] + jlist[:-1]
return k
def A257002_gen():
return (p for p in (prime(n) for n in count(1)) if pow(p, p, p + 2) == p)
def A258231_gen(startvalue=0):
return (
n
for n in count(max(startvalue, 0))
if n % 10 and set(str(n)) == set(str(n**2))
)
def A258456_gen(startvalue=1):
return (
i
for i in count(max(startvalue, 1))
if not integer_nthroot(i, 4)[1] and divisor_count(i) % 4
)
def A258786_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if sorted(str(n)) == sorted(str(sum(antidivisors(n))))
)
def A260031(n):
return int(gmpy2digits(n**n, 12).rstrip("0")[-1], 12)
def A260375_gen(): # generator of terms
yield 0
g = 1
for i in count(1):
g *= i
s = isqrt(g)
t = g - s**2
if is_square(t if t - s <= 0 else 2 * s + 1 - t):
yield i
def A260534_T(n, k):
return sum(0 if ~(k - j) & j else n**j for j in range(k + 1))
def A260597_gen(): # generator of terms
bset = set()
for n in count(1):
m = primefactors(
int(
"".join(
[str(d) for d in range(1, n + 1)]
+ [str(d) for d in range(n - 1, 0, -1)]
)
)
)
for p in m:
if not p in bset:
bset.add(p)
yield p
def A260796_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isprime(sum(int(d) for d in str(prime(n)) + str(prime(n + 1))))
)
def A261175_gen(): # generator of terms
n = 1
for i in count(0):
n *= i**i
yield len(str(n))
def A261534_gen(): # generator of terms
for m in pal_gen(3):
n = int(gmpy2digits(m, 3))
if n > 0 and not isprime(n) and (s := str(divisor_prod(n))) == s[::-1]:
yield n
def A261593_gen(): # generator of terms
for l in count(10):
for c in multiset_permutations("0" * (l - 10) + "1" * 10, l):
n = 2 * int("1" + "".join(c), 2)
if sum(int(d) for d in format(n * (n + 2), "b")) == 11:
yield n + 1
def A261694_gen(): # generator of terms
a, b, = (
0,
1,
)
while True:
yield a
a, b = b, (a + b) % 21
def A261749_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if sorted(str(n**2)) == sorted(str((n + 2) ** 2))
)
def A262776(n):
if n < 2:
return 0
a, b, m = 0, 1, factorial(fibonacci(n))
for i in range(factorial(n) - 1):
b, a = (b + a) % m, b
return b
def A350577_gen(): # generator of terms
p = 2
while True:
s = bin(p)[2:]
c, l = 0, len(s)
for i in range(l):
c += int(s[l - i - 1])
if 2 * c <= i:
break
else:
yield p
p = nextprime(p)
def A262814_gen(startvalue=1): # generator of terms
for k in count(max(startvalue, 1)):
n = k**k
if not n % k:
s = str(n)
for i in range(len(s) - 1):
s = s[1:] + s[0]
if int(s) % k:
break
else:
yield k
def A263400(n):
b, a = fib2(n)
s, m = gmpy2digits(b), n
while True:
a, b, m = b, a + b, m + 1
t = gmpy2digits(b)
if b > a and s in t:
return m
def A263457_gen(startvalue=1): # generator of terms
s = 0
for n in count(1):
s += divisor_count(n)
if is_square(8 * s + 1):
yield n
def A266001_gen():
return (
j
for j in (
int(format(i, "b"), 3) + (3**n - 1) // 2
for n in range(1, 10)
for i in range(2**n)
)
if "0" not in gmpy2digits(j, 4)
)
def A267140(n):
u, r, k, m = 2 * n + 1, 4 * n * (n + 1) + 1, 0, 2 * n + 1
while True:
if is_square(8 * m + r):
return m
k += 2
m += u + k
def A267767_gen():
return (int(s, 7) for s in (str(i**2) for i in count(0)) if max(s) < "7")
def A267818_gen():
return (
int(d, 4)
for d in (str(i**2) for i in count(1))
if max(d) < "4" and isprime(int(d, 4))
)
def A267982_gen(): # generator of terms
yield 0
b = 4
for n in count(1):
yield b
b = b * 4 * (n + 1) * (2 * n + 1) ** 2 // (n * (n + 2) ** 2)
def A268045(n):
if n == 0:
return 2
flist, k = Counter(factorint((n + 2) * (n + 1) // 2)), 2
while max(flist.values()) >= 2:
k += 1
flist += Counter(factorint(n + k))
flist -= Counter(factorint(k))
return k
def A268140(n):
p, n2 = 2, 2**n + 1
while True:
for i in range(1, n2):
if isprime(p + i):
p += i
break
else:
return p
def A268304_gen(): # generator of terms
b, m1, m2 = (
15,
[
21941965946880,
-54854914867200,
49244258396160,
-19011472727040,
2933960577120,
-126898662960,
771887070,
385943535,
385945560,
],
[
10569646080,
-25763512320,
22419210240,
-8309145600,
1209116160,
-46992960,
415800,
311850,
311850,
],
)
for n in count(0):
if b % 8 == 7:
yield 2 * n + 1
b = b * m1[-1] // m2[-1]
for i in range(8):
m1[i + 1] += m1[i]
m2[i + 1] += m2[i]
def A269903_gen(): # generator of terms
p = 1
for i in count(2):
p = (p * prime(i)) % 8
if p == 7:
yield i
def A269927_gen(): # generator of terms
yield 0
blist, c = [0], 1
while True:
ylist = [1 - d for d in blist]
zlist = list(blist)
for i in blist:
if i:
zlist += blist
else:
zlist += ylist
blist = zlist
yield from blist[c:]
c = len(blist)
def A270440_gen(): # generator of terms
b = 8
for n in count(0):
q, r = integer_nthroot(b + 1, 2)
yield (q + 1) // 2 + (0 if r else 1)
b = b * 2 * (2 * n + 1) // (n + 1)
def A271327_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
p, a, b = prime(n), 1, 1
for i in range(n):
if not a:
yield n
break
a, b = b, (a + b) % p
def A271899_gen(): # generator of terms
m = [88, -128, 61, -8] + [1] * 5
while True:
yield m[-1]
for i in range(8):
m[i + 1] += m[i]
def A272383_gen(startvalue=78): # generator of terms
for i in count(max(startvalue + (78 - startvalue % 78) % 78, 78), 78):
for d in divisors(i):
if d not in (1, 2, 6, 78) and isprime(d + 1):
break
else:
yield i
def A272673_gen():
return chain(
(0,),
(
int(str(m**2)[1:]) if sum(int(d) for d in str(m**2)[1:]) != 1 else 0
for m in count(4)
if str(m**2)[0] == "1"
),
)
def A272890_gen(startvalue=3):
return (
n
for n in count(max(startvalue, 3))
if sum(Fraction(n, a) for a in antidivisors(n)).denominator == 1
)
def A274951_gen(): # generator of terms
a, b = 8, 12
yield from [a, b]
for i in count(0):
c, d = divmod(b**2, a)
a, b = b, c + (0 if 2 * d < a else 1)
yield b
def A275465(n):
p = min(primefactors(n))
return p ** (n // p)
def A275544_gen(): # generator of terms
yield 1
c = [Fraction(0, 1)]
while True:
c = set(e for d in c for e in (3 * d + 1, d / 2))
yield len(c)
def A275628_gen(): # generator of terms
a, b = 31, 51
yield from [a, b]
for i in count(0):
c, d = divmod(b**2, a)
a, b = b, c + (0 if 2 * d < a else 1)
yield b
def A276389_gen(): # generator of terms
yield 0
m = 1
for n in count(1):
m *= n
s, h = str(m), hex(m)
if not len(s) - len(s.rstrip("0")) + len(h.rstrip("0")) - len(h):
yield n
def A276460_gen(): # generator of terms
yield 0
for m in count(0):
k = m**2 + 1
for d in divisors(k):
if d > m:
yield k
break
if not is_square(k // d - d):
break
def A276756_gen():
return chain(
(1,),
(
n
for n in count(2)
if max(factorint(n).values()) <= 1
and sum(Fraction(p, 10 ** len(str(p))) for p in primefactors(n)).denominator
== 1
),
)
def A277692(n):
return (
sum(1 for c in divisors(n - 1) if c < n - 1 and not (n * (n - 1) // 2) % c)
if n != 2
else 1
)
def A277937(n):
return sum(1 for d in bin(n)[2:].split("0") if len(d) == 1)
@lru_cache(maxsize=None)
def A278049(n):
if n == 0:
return -1
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * A278049(k1) - 1) // 3
j, k1 = j2, n // j2
return 3 * (n * (n - 1) - c + j) // 2 - 1
def A280056(n):
return (n**2 - (n % 2)) * (n - 1) * (n - 2) // 2
def A280660(n):
m, k, l = 10**n, 1, 2
while True:
if 2 * str(l).count("9") >= n:
return k
k += 1
l = (l * 2) % m
def A280717_gen(): # generator of terms
yield 3
n = 3
while True:
for i in range(1, n // 2 + 1):
j = i**2 + n * (n - i)
if isprime(j):
n = j
yield n
break
def A286328(n):
p, area = prime(n), 0
k, q, kq = (p + 1) // 2, (p**2 - 1) // 2, (p - 1) * (p + 1) ** 2 // 4
while True:
area += kq
if is_square(area):
return k
k += 1
kq += q
def A287298(n): # assumes 2 <= n <= 62
m = isqrt(mpz("".join(gmpy2digits(i, n) for i in range(n - 1, -1, -1)), n))
m2 = m**2
d = gmpy2digits(m2, n)
while len(set(d)) < len(d):
m -= 1
m2 -= 2 * m + 1
d = gmpy2digits(m2, n)
return m2
def A287609_gen(): # generator of terms
p, q, r = 2, 3, 5
while True:
n = p * (q + r) + q * r
m = n // 3
pm, nm = prevprime(m), nextprime(m)
k = n - pm - nm
if isprime(m):
if m == k:
yield n
else:
if nextprime(nm) == k or prevprime(pm) == k:
yield n
p, q, r = q, r, nextprime(r)
def A287686_gen(): # generator of terms
p2, q2, r2, r = 4, 9, 25, 5
while True:
n = p2 + q2 + r2
m = n // 3
pm, nm = prevprime(m), nextprime(m)
k = n - pm - nm
if isprime(m):
if m == k:
yield n
else:
if nextprime(nm) == k or prevprime(pm) == k:
yield n
s = nextprime(r)
p2, q2, r2, r = q2, r2, s**2, s
def A288507(n):
k, p, q = 1, 2, 3
while True:
if sum(factorint(q - p).values()) == n and sum(factorint(q + p).values()) == n:
return k
k += 1
p, q = q, nextprime(q)
def A289829_gen(startvalue=0): # generator of terms
a, b = integer_nthroot(startvalue, 2)
for n in count(max(a + (1 - int(b)), 0)):
m = n**2 - 1
for d in divisors(m):
if d * d >= m:
break
r = m // d
if not r % 2:
r = r // 2
if not isprime(r):
p, q = prevprime(r), nextprime(r)
if m == (q - p) * (q + p):
yield n**2
break
def A291175_gen(): # generator of terms
a, b, c = 1, 1, 2
for n in count(3):
if c == a + b:
yield n
a, b, c = b, c, reduced_totient(n + 1)
def A291199_gen(): # generator of terms
p = 3
while True:
if is_square(8 * (p - 1) * totient((p + 1) // 2) + 1):
yield p
p = nextprime(p)
def A292995(n):
return sum(int(d) for d in str(3**n)) // 9
def A294092_gen(): # generator of terms
m = 59
for k in count(119, 120):
if pow(2, m, k) == 1 and pow(3, m, k) == 1 and pow(5, m, k) == 1:
yield k
m += 60
def A295430(n):
m = 2 * n
while True:
if str(m)[0] == "3":
return m
m += n
def A295900_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if "2357" in str(n**3))
def A296516(n):
P, Q = {(1, 0)}, {(0, 1)}
for _ in range(n):
P, Q = P | Q, set((p[0] + q[0], p[1] + q[1]) for p in P for q in Q)
return len(Q)
def A297624_gen(): # generator of terms
b, c, aflag = 1, 2, False
for k in count(1):
cflag = isprime(c)
if aflag and cflag:
yield k
b, c, aflag = b + c, b + 2 * c, cflag
def A297815(n):
f = factorial(n)
return sum(
f // prod(factorial(d.count(a)) for a in set(d))
for d in combinations_with_replacement(range(1, 10), n)
if prod(d) == sum(d)
)
def A298077_gen():
return (
m
for m in (n * (n + 1) for n in count(3))
if prevprime(m // 2) + nextprime(m // 2) == m
)
def A298940(n):
if n == 1:
return 1
try:
return discrete_log(3**n - 2, -1, 3)
except ValueError:
return 0
def A299300_gen(): # generator of terms
p, d, n, r = 2, -1, 0, False
while True:
pn, k = p - n, d if r else -d
if 0 < k <= pn:
yield n + k
d += -pn if r else pn
r, n, p = not r, p, nextprime(p)
def A300817(n):
p, n2 = 2, n**2
if n % 2:
return 2 if isprime(2 + n2) else 0
while not isprime(p + n2):
p = nextprime(p)
return p
def A300902_gen(): # generator of terms
yield 1
m = 1
for n in count(1):
m *= n
yield m
if isprime(n):
m //= n
def A302292(n):
s = set()
for i in range(1, (n + 3) // 2):
for j in divisors(i):
for k in divisors(n - i):
if j != k:
s.add((min(j, k), max(j, k)))
return divisor_count(n) + 2 * len(s) - 1
def A302293(n):
s = set()
for i in range(1, n):
for j in divisors(i):
if integer_nthroot(j, 2)[1]:
for k in divisors(n - i):
s.add((j, k))
return len(s)
def A304290_gen(startvalue=0):
return (k for k in count(max(startvalue, 0)) if str(k - 1) in str(k**2))
def A305378(n):
m, tlist, s = 2 * n + 1, [1, 2, 4], 0
while tlist[-1] + tlist[-2] + tlist[-3] <= m:
tlist.append(tlist[-1] + tlist[-2] + tlist[-3])
for d in tlist[::-1]:
s *= 2
if d <= m:
s += 1
m -= d
return s
def A305884_gen(): # generator of terms
blist, n, m = [], 1, 1
while True:
for l in range(1, len(blist) + 1):
for d in multiset_combinations(blist, l):
if integer_nthroot(sum(d) + m, 2)[1]:
break
else:
continue
break
else:
blist.append(m)
yield m
continue
n += 1
m += 2 * n - 1
def A306043_gen(): # generator of terms
blist, n, m = [], 1, 1
while True:
for l in range(1, len(blist) + 1):
for d in combinations(blist, l):
if integer_nthroot(sum(d) + m, 2)[1]:
break
else:
continue
break
else:
blist.append(m)
yield m
n += 1
m += 2 * n - 1
def A306384(n):
mset, m, c = set(), n, 0
while True:
if m == 1 or m == 0 or m == 5:
return c
m = int(
"0"
+ "".join(
d
for d in split(
"(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)", str(2 * m)
)
if d != "" and d != None and len(d) == 1
)
)
if m in mset:
return -1
mset.add(m)
c += 1
def A306540(n):
if n == 1 or n == 10:
return 1
k, nk = 1, n
while True:
s = str(nk)
if s[:2] == "99" or s[:3] == "100":
return k
k += 1
nk *= n
def A306572_gen():
return (
n
for n, p in enumerate(primepi(k) for k in count(0))
if n > 0 and n % 10 ** len(str(p)) == p
)
def A307636_gen():
return filter(
lambda n: all(
len(set(s[0]) & set(s[1])) == 0
for s in combinations((str(d) for d in divisors(n, generator=True)), 2)
),
count(1),
)
def A308438(n):
l, p = 1, nextprime(n)
while True:
q = nextprime(p)
if q - p == 2 * n:
return p
p = q
if p >= (n + 1) * l:
l *= 10
p = nextprime(n * l)
def A308439(n):
return min(
primefactors(
1 + prod(prime(i + 1) for i, j in enumerate(bin(n)[:1:-1]) if j == "1")
)
)
def A308575(n):
n2, t1 = 2 ** (n - 1), 0
k = n2 - 1
kp = primepi(k)
kp2 = primepi(k + n2) - kp
while kp2 < kp or t1 >= kp:
k += n2
t1, t2 = kp, kp2
kp2 = primepi(k + n2) - kp2
kp = t2
return 2 * kp
def A308777(n):
if n == 1:
return 1
c, p = 0, prime(n)
p2, x = p**2, [prevprime(p), p, nextprime(p)]
while x[1] <= p2:
if x[1] - x[0] == 2 or x[2] - x[1] == 2:
c += 1
x = x[1:] + [nextprime(x[2])]
return c
def A308935(n):
n2, m, m2 = (
n**2 * (n**2 + 1),
n + 1,
((n + 1) ** 2 * ((n + 1) ** 2 + 1)) % (n**2 * (n**2 + 1)),
)
while m2:
m2, m = (m2 + 2 * (2 * m + 1) * (m**2 + m + 1)) % n2, (m + 1) % n2
return m
def A309388_gen(): # generator of terms
y, w = 1, 0
while True:
w += y
z = 0
for x in range(1, y + 1):
z += x
if is_square(8 * (w + z) + 1):
break
else:
yield y
y += 1
def A309387(n):
return gcd(n**2, harmonic(n - 1).p)
def A309851_gen():
return (m for m in (int(str(n) + str(2 * n - 1)) for n in count(1)) if isprime(m))
def A317977(n):
m = 2**n - 1
c = 4 % m
for _ in range(n - 2):
c = (c**2 - 2) % m
return c
def A318157_gen(): # generator of terms
for n in count(2):
if not (isprime(n) or isprime(n + 1) or isprime(n + 2) or isprime(n + 3)):
if isprime(4 * n + 5):
yield 4 * n + 5
if isprime(4 * n + 7):
yield 4 * n + 7
def A318972(n):
return (
(7 * n + 1) // 4 if n % 4 == 1 else (7 * n - 1) // 4 if n % 4 == 3 else n // 2
)
def A319228(n):
c, b, b2, n10 = 0, 1, 3, 10**n
while b <= n10:
if isprime(b2):
c += 1
b += 1
b2 += 2 * b
return c
def A320909_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isprime(int(str(n**2)[::-1])) and isprime(int(str(n**3)[::-1]))
)
def A320920(n):
w, m = int(factorial(n)), n
bc = [comb(n - 1, i) % w for i in range(n + 1)]
while True:
bc[n] = (bc[n - 1] + bc[n]) % w
if bc[n] == 0:
return m
for i in range(n - 1, 0, -1):
bc[i] = (bc[i - 1] + bc[i]) % w
m += 1
def A321685(n):
return Matrix(n, n, [composite(i) for i in range(1, n**2 + 1)]).det()
def A322250(n):
s = bin(2 * n - 1)[2:].rstrip("1")
return int(s, 2) if s != "" else 1
def A322743(n):
i = 4 if n <= 1 else 2**n + 1
j = 1 if n <= 2 else 2
while True:
if not isprime(i):
c = 0
for m in range(len(bin(i)) - 2):
if isprime(i ^ (2**m)):
c += 1
if c > n:
break
if c == n:
return i
i += j
def A323026_gen():
return (
n
for n in (
int("".join(s)) for l in count(9) for s in permutations("123456789", l)
)
if isprime(n - 1) and isprime(n + 1)
)
def A323062_gen(startvalue=1):
return (
k
for k in count(max(startvalue, 1))
if (2 * isqrt(2 ** (2 * k - 1)) - 1) ** 2 > 1 + 4 * (2 ** (2 * k - 1) - 2**k)
)
def A323278_gen(): # generator of terms
p, nmax = 2, -1
while True:
n = divisor_count(p**2 - 1)
if n > nmax:
nmax = n
yield p**2 - 1
p = nextprime(p)
def A324309(n):
m, k = 2, 2**n
while True:
s = str(k)
for i in range(1, len(s)):
if s[i] == s[i - 1]:
return m
m += 1
if m % 10 == 0:
m += 1
k = m**n
def A328131(n):
s, tlist = str(n), ("2468", "369", "468", "5", "689", "7", "8", "9")
dset = set(
"0"
+ "".join(
t if t[0] in s and sum(s.count(d) for d in t) > 1 else "" for t in tlist
)
)
return int("0" + "".join(d for d in s if d not in dset))
def A328375_gen(startvalue=0):
return (k for k in count(max(startvalue, 0)) if "777" in str(2**k))
def A328947_geh():
return (n for n in (int(bin(m)[2:]) for m in count(0)) if not n % 7)
def A330243_gen(startvalue=0):
return (n for n in count(0) if str(2**n)[0] == "7")
@lru_cache(maxsize=None)
def A330503(n):
if n == 0:
return 0
c, j = 0, 2
k1 = n // j
while k1 > 1:
j2 = n // k1 + 1
c += (j2 - j) * (2 * A330503(k1) // (k1 + 1) - 1)
j, k1 = j2, n // j2
return (n + 1) * (n * (n - 1) - c + j) // 2
def A331988_T(n, k): # compute T(n,k)
if k == 1:
count = 1
for i in range(1, n):
count *= i + 1
return count
ntuple, count = tuple(range(1, n + 1)), 0
for s in combinations_with_replacement(permutations(ntuple, n), k - 2):
t = list(ntuple)
for d in s:
for i in range(n):
t[i] += d[i]
t.sort()
w = 1
for i in range(n):
w *= (n - i) + t[i]
if w > count:
count = w
return count
def A332842(n):
m, k = 1, 1
for i in range(2, n + 1):
k *= i
m *= k
return int(str(m)[0])
def A333445_T(n, k): # compute T(n,k)
c, l = 1, list(range(1, k * n + 1, k))
lt = list(l)
for i in range(n):
for j in range(1, k):
lt[i] += l[i] + j
c *= lt[i]
return c
def A333596_gen():
return accumulate(A334841(n) for n in count(0))
def A333975_gen(): # generator of terms
yield from [1, 2]
blist, bset, m = [1, 2], set(), 2
for i in count(3):
for j in range(i - 2):
bset.add(m | blist[j])
m += 1
while m in bset:
m += 1
blist.append(m)
yield m
def A334042(n):
return 2 ** (len(bin(n**2)) - 2) - 1 - n**2
def A334076(n):
m = n | (2 * n)
return 0 if n == 0 else 2 ** (len(bin(m)) - 2) - 1 - m
def A334116_helper(w, m):
a, p, s, vv = m, 0, w, []
while a < 2 * m:
p += 1
s = S.One / (s - floor(s))
a = floor(s)
if a < 2 * m:
vv.append(a)
j = (p - 1) // 2
v = [0, 1, 1] if p % 2 else [1, 0, vv[j]]
for i in range(j - 1, -1, -1):
h = vv[i]
v = [v[0] + h * v[2], v[2], 2 * h * v[0] + v[1] + h**2 * v[2]]
return v
def A334116(n):
w = sqrt(n)
m = floor(w)
if w == m:
return n
else:
x, y, z = A334116_helper(w, m)
if z % 2:
x *= 2
else:
z //= 2
y //= 2
return (m + z) ** 2 + x + (x * m + y) // z
@lru_cache(maxsize=None)
def A334535(n):
if n <= 2:
return n
i, a, b = 2, A334535(n - 1), A334535(n - 2)
q = b
while q >= n:
i += 1
q = A334535(n - i)
return 2 * A334535(q) + a - b
def A335306(n):
p = prime(n)
for m in range(max(4, 2 * p - 4), p**2 + 1):
if sum(primefactors(m)) == p:
return m
def A335313(n):
m = 2 ** (3 * 2**n)
p = prevprime(m)
while not isprime((p - 1) // 2):
p = prevprime(p)
return m - p
def A335940(n):
if isprime(n):
return n
else:
pf = primefactors(n)
return max(pf) - min(pf)
def A336257_gen(): # generator of terms
yield from [0, 1]
c = 1
for n in count(2):
c = c * (4 * n - 2) // (n + 1)
yield c % (2 * n + 1)
def A337098(n):
k = 1
while True:
if n == sum(
1
for x in combinations((d**3 for d in divisors(k)), 4)
if sum(x[:-1]) == x[-1]
):
return k
k += 1
def A337212(n):
x, y, k, r, m = (3**n - 3) // 2, (3**n - 3) // 2, (n - 1) % 3, 3 ** (n - 1), 0
while True:
m += 1
a, b = divmod(x, 3)
x, k = a + k * r, (k + k - b) % 3
if y == x:
return m
def A339566_gen(): # generator of terms
p = 2
while True:
if int(bin(p)[2:]) % p == 1:
yield p
p = nextprime(p)
def A340290_gen():
return (
int(s)
for s in (gmpy2digits(prime(i), 3) for i in count(1))
if isprime(int(s, 4))
)
def A340479(n):
s = str(n)
return int(s[::-1]) + sum(int(d) for d in s)
def A340768(n):
return divisors(composite(n))[2]
def A350093_gen(): # generator of terms
a, b = divisor_count(1), divisor_count(2)
for k in count(1):
if a + b == 6:
yield k
a, b = b, divisor_count(k + 2)
def A340876_gen(): # generator of terms
p, q, r, s = 2, 3, 5, 7
for k in count(1):
if pow(p, q, s) == r:
yield k
p, q, r, s = q, r, s, nextprime(s)
def A341115_gen(): # generator of terms
m, l, n = 2**101, 2**101 + 1, 10**100
for k in count(1):
if pow(10, n, l) == l - 1:
yield k
l += m
def A341276(n):
return (
1
+ 3 * n * (n + 1)
- 2 * sum(n // k for k in range(1, isqrt(n) + 1))
+ isqrt(n) ** 2
)
def A341700(n):
s, m = 0, nextprime(n)
while m <= 2 * n:
s += m
m = nextprime(m)
return s
def A342025(n):
f = factorint(n)
return int(
sum(b for a, b in f.items() if a % 4 == 3)
== sum(b for a, b in f.items() if a % 4 == 1)
)
def A342081_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if len([p for p in primefactors(n) if p > 2 and p * p <= n]) == 0
)
def A342082_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if len([p for p in primefactors(n) if p > 2 and p * p <= n]) > 0
)
def A342175(n):
m = composite(n)
k = m + 1
while gcd(k, m) != 1 or isprime(k):
k += 1
return k - m
def A342308_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if set(str(n**5)) == {"1", "2", "3", "4", "5", "6", "7", "8", "9"}
)
def A342403(n):
return 1 if n == 1 else -sum(d * A342403(d) for d in divisors(n) if d < n)
def A342601_gen(): # generator of terms
m, s = 2, str(2**10)
for k in count(1):
if s in str(m):
yield k
m *= 2
def A342851_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if n == 0 or n % 10)
def A342871(n):
c = 0
for k in range(1, n + 1):
m = integer_nthroot(n, k)[0]
if m == 1:
return c + n - k + 1
else:
c += m
return c
def A342892(n):
s = bin(n)[2:]
m = len(s)
i = s[::-1].find("1")
return 1 - int(s[m - i - 3]) if m - i - 3 >= 0 else 1
def A342906(n):
return 2 ** (2 * n - 2) - catalan(n)
def A343128_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if n % 2 and n % 5 and prime(prime(prime(n))) % 10 ** (len(str(n))) == n
)
def A343145(n):
k = 1
while True:
m = k
for _ in range(n):
m = prime(m)
if m % 10 ** (len(str(k))) == k:
return k
k += 1
while not (k % 2 and k % 5):
k += 1
@lru_cache(maxsize=None)
def A343493(n):
return 1 - sum(A343493(d - 1) for d in divisors(n) if d < n)
def A343507(n):
k, f = 0, Fraction(1, int(factorial(n)) ** 2)
while f.denominator != 1:
k += 1
f *= Fraction(2 * k * (2 * k - 1), (k + n) ** 2)
return k
def A343536_gen(): # generator of terms
s = "1"
for k in count(1):
if str(k**2) in s:
yield k
s += str(k + 1)
def A343727_gen():
return (
n
for n in (int("".join(d)) for l in count(1) for d in product("13579", repeat=l))
if set(str(n**2)[:-1]) <= set("02468")
)
def A343731_gen(): # generator of terms
yield 0
c = 0
for n in count(2):
x = prod(n * d + 1 for d in factorint(n).values())
if x > c:
c = x
yield n
def A343780(n):
q = 1
while True:
s, c = [1] * n + [0] * n, 0
for i in range(n):
c = (c + q) % (2 * n - i)
if s[c]:
break
s = s[:c] + s[c + 1 :]
else:
return q + 1
q += 1
def A343802(n):
s, c = 0, 0
while s < 10**n:
c += 1
s += totient(c)
return c
def A344013_gen(): # generator of terms
yield 1
b = 1
while True:
b = sum(ord(s) - 96 for s in unidecode(num2words(b, lang="fr")) if s.isalpha())
yield b
def A344421(n):
return sum(
floor(n * sin(x * pi / n)) - int((n * sin(x * pi / n)).is_integer == True)
for x in range(1, n)
)
def A344478(n):
fs = factorint(n)
return 0 if len(fs) == 0 or max(fs.values()) > 1 else len(fs)
def A344856(n):
return prime(n) ^ n**2
def A344888(n):
b, m = 2, n
while True:
m, x = divmod(m, b)
m, y = divmod(m, b)
while m > 0:
m, z = divmod(m, b)
if z != x:
break
if m > 0:
m, z = divmod(m, b)
if z != y:
break
else:
return b
else:
return b
b += 1
m = n
def A344949(n):
return min(d[1] ** 2 for d in diop_DN(4 * n + 2, 1)) // 4
def A344985(n):
s, c, b = bin(n)[2:], 0, 0
for x in s:
b += 1 if x == "1" else -1
c += abs(b)
return c
def A345299(n):
return sum(p ** primepi(p) for p in primefactors(n))
def A345301(n):
return sum(p ** primepi(n // p) for p in primefactors(n))
def A345348_gen():
return (
n
for n in (m * (m + 1) // 2 for m in count(0))
if len(bin(n)) - 2 == 2 * bin(n).count("1")
)
def A345420(n):
return igcdex(5, prime(n))[0]
def A345696(n):
zlist = [
z
for z in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if z[2] == 1
]
return pvariance(len(zlist) * (u**2 + v**2) for u, v, w in zlist)
def A345724(n):
return pvariance(
n**2 * (u + v)
for u, v, w in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
)
def A345725(n):
zlist = [
z
for z in (igcdex(x, y) for x in range(1, n + 1) for y in range(1, n + 1))
if z[2] == 1
]
return pvariance(len(zlist) * (u + v) for u, v, w in zlist)
def A346147_gen(): # generator of terms
p, q = 2, 3
while True:
if isprime(p * q % (p + q)) and isprime(p * q // (p + q)):
yield p
p, q = q, nextprime(q)
def A346203(n):
m, k, p, s = 1, 0, 1, str(n)
while s not in str(m):
k += 1
p = nextprime(p)
m *= p
return k
def A346528(n):
if n == 1:
return 17
a, b, k, k2, m, r, s = -6 * (n + 1) ** 2, (n + 1) ** 4, 2, 4, 1, 0, 0
while 2 * m + a < 0 or m * (m + a) + b < 0:
if isqrt(2 * m) - isqrt(m - 1) == n:
r = m
if s == 0 and isqrt(2 * m + 2) - isqrt(m) == n:
s = m
k += 1
k2 += 2 * k - 1
m = (k2 - 1) // 2
return r - s
def A347274(n):
return 1 if n == 1 else n**2 * (n**n - n) // (n - 1) ** 2
def A347275(n):
return (
2 * n + 1
if n <= 1
else 2 * (n + sum(n // k for k in range(1, isqrt(n) + 1))) - isqrt(n) ** 2 - 1
)
def A347304(n):
return factorial(n) // factorial(n // 2) // factorial(n // 3) // factorial(n // 6)
def A347314_gen(): # generator of terms
yield 1
nset, m, j = {1}, 2, 2
for i in count(2):
k = m
while k == j or gcd(k, j) == 1 or k in nset:
k += 1
if i == k:
yield i
j = k + 1
nset.add(k)
while m in nset:
m += 1
def A347815_gen():
return (
p
for p in (prime(n) for n in count(3))
if legendre_symbol(30, p) == legendre_symbol(105, p) == -1
)
def A347816_gen():
return (
p
for p in (prime(n) for n in count(3))
if legendre_symbol(15, p) == legendre_symbol(85, p) == -1
)
def A348017_gen(startvalue=0):
return (
k
for k in count(max(startvalue, 0))
if isprime((lambda x: x.p % x.q)(harmonic(k)))
)
def A022510_gen(): # generator of terms
yield 6
l = "6"
while True:
l = "".join(
str(len(d)) + d[0]
for d in split("(0+|1+|2+|3+|4+|5+|6+|7+|8+|9+)", l[::-1])
if d
)
yield int(l)
def A058994_gen(): # generator of terms
m = 7
for k in count(1):
if isprime(int(str(m)[::-1])):
yield k
m *= 7
def A058995_gen(): # generator of terms
m = 13
for k in count(1):
if isprime(int(str(m)[::-1])):
yield k
m *= 13
def A093502_gen(): # generator of terms
yield 2
p, q = 2, 1
while True:
r = p + q
p, q = prime(r), r
yield p
def A108860_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not sum(int(d) for d in str((2 * n) ** n)) % n
)
def A109675_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if not sum([int(d) for d in str(n**n - 1)]) % n
)
def A112258_gen(startvalue=1):
return (
n for n in count(max(startvalue, 1)) if n % 10 and len(set(str(n**26))) < 10
)
def A123911_gen(): # generator of terms
plist = [0] + [prime(i) for i in range(1, 10)]
for l in count(1):
L = 10 ** (l - 1)
H = 10 * L
for c in combinations_with_replacement(range(1, 10), l):
n = prod(plist[i] for i in c) + sum(c)
if L <= n < H and sorted(int(d) for d in str(n)) == list(c):
yield n
def A126703_gen(startvalue=1):
return (n for n in count(max(startvalue, 1)) if isprime(pow(n, n, 10**n)))
def A137019_gen():
return (
n
for n in (int("".join(d)) for l in count(1) for d in product("1279", repeat=l))
if set(str(n**2)) <= set("1279")
)
def A143992_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if n != 4
and not isprime(n)
and str(sum(a * b for a, b in factorint(n).items())) in str(n)
)
def A155012_gen(): # generator of terms
a, b, a2, b2 = 0, 1, 2, 5
while True:
if isprime(b) and isprime(b2):
yield b
a, b, a2, b2 = b, a + b, b2, a2 + b2 - 2
def A175975_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if str(n**n).count("1") == 2)
def A246421_gen(startvalue=1):
for n in count(max(startvalue, 1)):
s = str(n)
if not s.count("0"):
s2 = sorted(s)
if s2 == sorted(str(n + sum(int(d) for d in s))) and s2 == sorted(
str(n + prod(int(d) for d in s))
):
yield n
def A247047_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if len(set(str(n**3))) == 3 and len(set(str(n**2))) == 2
)
def A248135_gen(startvalue=1):
for n in count(max(startvalue, 1)):
if not isprime(n):
a = sum([int(n * e / p) for p, e in factorint(n).items()]) if n > 1 else 0
if not sum(a % i for i in range(1, a)) % n:
yield n
def A255669_gen(): # generator of terms
p1, p2, l = 2, 3, 10
for n in count(0):
p3 = nextprime(p2)
if p3 >= l: # this test is sufficient due to Bertrand-Chebyshev theorem
l *= 10
if not ((p2 % p1) * l + p3) % p1:
yield p1
p1, p2 = p2, p3
def A259630_gen(): # generator of terms
bset, k = set(), 0
while True:
n, m = 0, 1
k += m
while n in bset or not isprime(k):
n += 1
k += m
m *= 2
bset.add(n)
yield n
def A260097_gen(startvalue=11): # generator of terms
for n in count(max(startvalue, 11)):
s = str(n)
for l in range(1, len(s)):
m = int(s[:l]) * int(s[l:])
if m > 0 and n == divisor_sigma(m):
yield n
break
def A261459_gen(startvalue=0):
return (
k
for k in count(max(startvalue, 0))
if is_prime(int("1" * k + str(k * (k + 1) + 1) + "1" * k))
)
def A264725_gen(): # generator of terms
c, n, m, k = 3, 7, 29927007, 10**8
while True:
if isprime(n):
yield c
c += 8
n = n * k + m
def A268511_gen(startvalue=1): # generator of terms
for n in count(max(startvalue + 1 - startvalue % 2, 1), 2):
m = factorint(3**n + 5**n)
for d in m:
if d % 4 == 3 and m[d] % 2:
break
else:
yield n
def A268517_gen(): # generator of terms
yield 321
a = 321
for i in count(0):
a = (
((a + 1 + (2 - i) % 3) % 10) * 100
+ ((a // 100 + 1 + (-i) % 3) % 10) * 10
+ ((a // 10 + 1 + (1 - i) % 3) % 10)
)
yield a
def A270538_gen():
return (
n**2
for n in range(10**6)
if n == sum(int(a) ** (b + 1) for b, a in enumerate(str(n**2)))
)
def A276718_gen(): # generator of terms
q = 0
for i in count(1):
s = str(i)
q += Fraction(int(s[::-1]), 10 ** len(s))
if q.denominator == 1:
yield i
def A291340_gen(): # generator of terms
yield 2
p = 3
while True:
if is_square(8 * (p - 1) * totient((p - 1) // 2) + 1):
yield p
p = nextprime(p)
def A297710_gen(): # generator of terms
for i in count(1):
n = npartitions(i)
s = [int(d) for d in str(n)]
for j in range(len(s) - 1):
if not (s[j] + s[j + 1]) % 2:
break
else:
yield n
def A306666_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if is_square(n * (n * (n * (n * (n - 9) + 33) - 58) + 42))
)
def A318189(n):
r, q = n % 2, 2
while True:
c, m = 0, q
for i in range(n + 1):
c += m
m = prime(m)
if is_prime(r + c):
return q
q = nextprime(q)
def A322047_gen(startvalue=0):
return (n for n in count(max(startvalue, 0)) if "e" not in num2words(n, lang="fi"))
def A311481(n):
return ord(unidecode.unidecode(num2words(n, to="ordinal")).lower()[0]) - 96
def A311482(n):
return ord(unidecode.unidecode(num2words(n, lang="nl")).lower()[0]) - 96
def A311498(n):
return ord(unidecode.unidecode(num2words(n, lang="fr")).lower()[0]) - 96
def A332242_gen(): # generator of terms
n = 1
for i in count(0):
s = str(n)
if len(s) - s.count("0") == i:
yield i
n *= i + 1
def A333122_gen(): # generator of terms
plist = [2, 3, 5, 7, 11, 13]
while True:
m = plist[0] + plist[5]
if m == plist[1] + plist[4]:
yield m
plist = plist[1:] + [nextprime(plist[-1])]
def A333390_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if isprime(primorial(2 * n, nth=False) * 2**n - 1)
)
def A335361_gen(): # generator of terms
p = 2
while True:
f, g = factorial(p), 1
for i in range(1, p + 1):
g += f
if isprime(g):
break
else:
yield p
p = nextprime(p)
def A337508_gen(): # generator of terms
p = 11
while True:
s = str(p)
l = len(s) // 2
if not (isprime(int(s[:l])) or isprime(int(s[-l:]))):
yield p
p = nextprime(p)
def A339174_gen(): # generator of terms
yield 2
a = 2
while True:
c, b = 1, (a - 1) * a
for k in count(1):
c += b
if isprime(c):
yield k
a = c
break
def A340431_gen(): # generator of terms
p = 2
while True:
q = nextprime(p)
if q > p + 2:
pq = p + q
if pow(q, p, pq) == q and pow(p, q, pq) == p:
yield p
p = q
def A340466_gen():
return (
p
for p in (prime(n) for n in count(1))
if len(bin(p)) - 2 < 2 * bin(p).count("1") < 2 * len(bin(p)) - 4
)
def A000201(n):
return (n + isqrt(5 * n**2)) // 2
def A185381(n):
return fibonacci((n + isqrt(5 * n**2)) // 2)
def A350678(n):
return sum(fibonacci((i + isqrt(5 * i**2)) // 2) for i in range(n + 1))
def A342118_gen(): # generator of terms
plist = [Fraction(1, totient(i)) for i in range(1, 7)]
p = sum(plist)
for k in count(1):
if p.numerator == 1:
yield k
p -= plist[0]
plist = plist[1:] + [Fraction(1, totient(k + 6))]
p += plist[-1]
def A342221_gen(startvalue=1): # generator of terms
for k in count(max(startvalue, 1)):
if k % 3 != 1:
m, l = (10**k - 1) // 9, 2
for i in range(k):
if isprime(m + l):
break
l *= 10
else:
yield k
def A342349_gen():
p = 2
while True:
q = p**3
C1, C2 = Counter(s := str(p)), Counter(str(q))
if all(C1[d] <= C2[d] for d in s):
yield q
p = nextprime(p)
def A342503_gen(startvalue=1):
return (
k
for k in count(max(startvalue, 1))
if sum(k % i for i in range(1, k // 2 + 1) if gcd(i, k) == 1) % k == 0
)
def A342809_gen(startvalue=1):
return (
k
for k in count(max(startvalue, 1))
if isprime(k - 1) and isprime(k // 5 + int(k % 5 > 2))
)
def A343011_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if (divisor_sigma(n, 0) * divisor_sigma(n, 2) - divisor_sigma(n, 1) ** 2)
% divisor_sigma(n, 0) ** 2
== 0
)
def A343732_gen(startvalue=2):
return (
n
for n in count(max(startvalue, 2))
if len(factorint(prod(n * d + 1 for d in factorint(n).values()))) == 1
)
def A344202_gen(): # generator of terms
p = 5
while True:
if gcd(n_order(2, p), n_order(3, p)) == 1:
yield p
p = nextprime(p)
def A000040(n):
return prime(n)
def A000079(n):
return 2**n
def A000142(n):
return factorial(n)
def A001222(n):
return sum(factorint(n).values())
def A007318_T(n, k):
return comb(n, k)
def A001221(n):
return len(factorint(n))
def A001358_gen(startvalue=2):
return (n for n in count(max(startvalue, 2)) if A001222(n) == 2)
def A000720(n):
return primepi(n)
def A002110(n):
return 1 if n == 0 else primorial(n)
def A034386(n):
return 1 if n == 0 else primorial(n, nth=False)
def A008683(n):
return mobius(n)
def A000032(n):
return lucas(n)
def A000225(n):
return 2**n - 1
def A002275(n):
return (10**n - 1) // 9
def A005408(n):
return 2 * n + 1
def A006530(n):
return 1 if n == 1 else max(primefactors(n))
def A020639(n):
return 1 if n == 1 else min(primefactors(n))
def A000984(n):
return comb(2 * n, n)
def A000292(n):
return comb(n + 2, 3)
def A000290(n):
return n**2
def A000244(n):
return 3**n
def A002378(n):
return n * (n + 1)
def A005843(n):
return 2 * n
def A000129_gen(): # generator of terms
a, b = 0, 1
yield from [a, b]
while True:
a, b = b, a + 2 * b
yield b
def A000041(n):
return npartitions(n)
def A001045_gen(): # generator of terms
a, b = 0, 1
yield from [a, b]
while True:
a, b = b, 2 * a + b
yield b
def A000043_gen():
return (p for p in (prime(n) for n in count(1)) if isprime(2**p - 1))
def A008277_T(n, k):
return stirling(n, k)
def A000396_gen():
return filter(lambda n: divisor_sigma(n) == 2 * n, count(1))
def A010060_gen(): # generator of terms
yield 0
blist = [0]
while True:
c = [1 - d for d in blist]
blist += c
yield from c
def A000312(n):
return n**n
def A000326(n):
return n * (3 * n - 1) // 2
def A000302(n):
return 4**n
def A001065(n):
return divisor_sigma(n) - n
def A000330(n):
return n * (n + 1) * (2 * n + 1) // 6
def A002620(n):
return n**2 // 4
def A004526(n):
return n // 2
def A001405(n):
return comb(n, n // 2)
def A001405_gen(): # generator of terms
yield 1
a = 1
for i in count(1):
a = 2 * a * i // (i + 1) if i & 1 else 2 * a
yield a
def A001764(n):
return comb(3 * n, n) // (2 * n + 1)
def A000124(n):
return n * (n + 1) // 2 + 1
def A350536(n):
m = 2 * n + 1
for l in count(len(str(m))):
for s in product("13579", repeat=l):
k = int("".join(s))
if k > m and k % m == 0:
return k
def A350538(n):
for l in count(len(str(n)) - 1):
for a in "2468":
for b in product("02468", repeat=l):
k = int(a + "".join(b))
if k > n and k % n == 0:
return k
def A350654(n):
for m in count(2):
c = 0
for d in divisors(m, generator=True):
if not (
((m - 1) % (d - 1) if d > 1 else True)
and (m - 1) % (d + 1)
and ((m + 1) % (d - 1) if d > 1 else True)
and (m + 1) % (d + 1)
):
c += 1
if c > n:
break
if c == n:
return m
def A078221(n):
return 2 * n - 1 if n < 3 else 10 ** (2 ** (n - 3)) - 1
def A350540(n):
return min(sqrt_mod(17, 2**n, all_roots=True))
def A350549(n):
return 1 if n == 0 else Matrix(n, n, lambda i, j: (j - i + 1) // 2).per()
def A350603_gen(): # generator of terms
s = {0}
while True:
yield from sorted(s)
s = set(chain.from_iterable((x + 1, 2 * x) for x in s))
def A000203(n):
return divisor_sigma(n)
def A027641(n):
return bernoulli(n).p
def A027642(n):
return bernoulli(n).q
def A122554_gen(): # generator of terms
s = {1}
while True:
yield len(s)
s = set(chain.from_iterable((x, x + 2, 2 * x) for x in s))
def A123212_gen(): # generator of terms
s = {1}
while True:
yield sum(s)
s = set(chain.from_iterable((x, 2 * x, x**2) for x in s))
def A123247_gen(): # generator of terms
s = {1}
while True:
yield len(s)
s = set(chain.from_iterable((x, x + 1, 2 * x, 3 * x) for x in s))
def A350604_gen(): # generator of terms
s = {1}
while True:
yield from sorted(s)
s = set(chain.from_iterable((x, 2 * x, 3 * x) for x in s))
def A350605_gen(): # generator of terms
s = {1}
while True:
yield from sorted(s)
s = set(chain.from_iterable((x, 2 * x + 1, 3 * x + 1) for x in s))
def A350606_gen(): # generator of terms
s = {1}
while True:
yield len(s)
s = set(chain.from_iterable((x, 2 * x + 1, 3 * x + 1) for x in s))
def A000272(n):
return 1 if n <= 1 else n ** (n - 2)
def A001157(n):
return divisor_sigma(n, 2)
@lru_cache(maxsize=None)
def A002033(n):
if n <= 1:
return 1
return sum(A002033(i - 1) for i in divisors(n + 1, generator=True) if i <= n)
def A005834(n):
return 2 * n
def A350246_gen(): # generator of terms
yield 11
s = "11"
while True:
for k in count(3, 3):
t = str(k)
m = int(t + s)
if isprime(m) and isprime(m + 2):
yield k
break
s = t + s
def A350691_helper(
n, m
): # generator in order of numbers with n decimal digits and m 1's. leading zeros are allowed.
if n >= m:
if n == 1:
if m == 1:
yield 1
else:
yield 0
yield from range(2, 10)
elif n == m:
yield (10**m - 1) // 9
else:
for b in A350691_helper(n - 1, m):
yield b
r = 10 ** (n - 1)
for b in A350691_helper(n - 1, m - 1):
yield r + b
for a in range(2, 10):
k = a * r
for b in A350691_helper(n - 1, m):
yield k + b
def A350691(n):
for l in count(n):
r = 10 ** (l - 1)
for a in range(1, 10):
n2 = n - 1 if a == 1 else n
k = a * r
for s in A350691_helper(l - 1, n2):
m = k + s
if bin(m)[2:].count("1") == n:
return m
def A350692_helper(
n, m
): # generator in order of numbers with n decimal digits and m 0's. leading zeros are allowed.
if n >= m:
if n == 1:
if m == 1:
yield 0
else:
yield from range(1, 10)
elif n == m:
yield 0
else:
for b in A350692_helper(n - 1, m - 1):
yield b
r = 10 ** (n - 1)
for a in range(1, 10):
k = a * r
for b in A350692_helper(n - 1, m):
yield k + b
def A350692(n):
if n == 1:
return 0
for l in count(n):
r = 10 ** (l - 1)
for a in range(1, 10):
k = a * r
for s in A350692_helper(l - 1, n):
m = k + s
if bin(m)[2:].count("0") == n:
return m
@lru_cache(maxsize=None)
def A000364(n):
return (
1
if n == 0
else (1 if n % 2 else -1)
* sum((-1 if i % 2 else 1) * A000364(i) * comb(2 * n, 2 * i) for i in range(n))
)
def A000688(n):
return prod(map(npartitions, factorint(n).values()))
def A000262_gen(): # generator of terms
a, b = [1, 1]
yield from [1, 1]
for n in count(2):
a, b = b, (2 * n - 1) * b - (n - 1) * (n - 2) * a
yield b
def A000262(n):
return hyperexpand(hyper((-n + 1, -n), [], 1))
@lru_cache(maxsize=None)
def A001462(n):
return 1 if n == 1 else 1 + A001462(n - A001462(A001462(n - 1)))
def A005100_gen(startvalue=1):
return filter(lambda n: divisor_sigma(n) < 2 * n, count(max(startvalue, 1)))
def A005101_gen(startvalue=1):
return filter(lambda n: divisor_sigma(n) > 2 * n, count(max(startvalue, 1)))
@lru_cache(maxsize=None)
def A001190(n):
if n <= 1:
return n
m = n // 2 + n % 2
return (
sum(A001190(i + 1) * A001190(n - 1 - i) for i in range(m - 1))
+ (1 - n % 2) * A001190(m) * (A001190(m) + 1) // 2
)
def A008292_T(n, k):
return sum(
(-1 if j % 2 else 1) * (k - j) ** n * comb(n + 1, j) for j in range(k + 1)
)
@lru_cache(maxsize=None)
def A000081(n):
return (
n
if n <= 1
else sum(
sum(d * A000081(d) for d in divisor_tuple(k)) * A000081(n - k)
for k in range(1, n)
)
// (n - 1)
)
def A350738(n):
return Poly(
sum(
(-1 if k % 2 else 1)
* symbolx ** (k**2)
* prod(1 + symbolx**j for j in range(1, k + 1))
for k in range(isqrt(n + 1) + 1)
)
).all_coeffs()[-n - 1]
def A014258_gen(): # generator of terms
a, b = 0, 1
yield 0
while True:
yield b
a, b = b, int(str(a + b)[::-1])
def A350079_gen(): # generator of terms
a, b = 0, 1
for n in count(1):
if b < a:
yield n
a, b = b, int(str(a + b)[::-1])
def A350782(n):
m, p, c = factorial(n), 3, 0
while p <= m:
if isprime(2 * m - p):
c += 1
p = nextprime(p)
return c
def A350743(n):
f = list(factorint(n).items())
return sum(
1
for k in range(1, n + 1)
if prod(p ** ((q + 1) * k) - 1 for p, q in f)
// prod(p**k - 1 for p, q in f)
% k
== 0
)
def A018819_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (1, 1, 2, 2, 4, 4)
while True:
a += b
yield from (2 * a,) * 2
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
@lru_cache(maxsize=None)
def A018819(n):
return 1 if n == 0 else A018819(n - 1) + (0 if n % 2 else A018819(n // 2))
def A000123_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (1, 2, 4)
while True:
a += b
yield 2 * a
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
@lru_cache(maxsize=None)
def A000123(n):
return 1 if n == 0 else A000123(n - 1) + A000123(n // 2)
def A350493(n):
return pow(isqrt(prime(n)), 2, n)
def A054108(n):
return (1 if n % 2 else -1) * sum(
(-1 if k % 2 else 1) * comb(2 * k, k) for k in range(n + 2)
)
def A054108_gen(): # generator of terms
b = 1
for n in count(1):
b = comb(2 * n, n) - b
yield b
def A349554(n):
return (1 if n % 2 else -1) * (
sum((-1 if k % 2 else 1) * comb(2 * k, k) for k in range(n + 2)) - 4
)
def A349554_gen(): # generator of terms
b = 5
for n in count(2):
b = comb(2 * n, n) - b
yield b
def A350459(n):
return sum(
1
for d in range(1, n + 1)
for c in range(1, n + 1)
for b in range(1, d + 1)
for a in range(1, b + 1)
if (a * d) ** 2 + (b * c) ** 2 == (c * d) ** 2
)
def A350247_gen(startvalue=3): # generator of terms
for n in count(max(3, startvalue + (3 - startvalue % 3) % 3), 3):
if isprime(100 * n + 11) and isprime(100 * n + 13):
yield n
def A010051(n):
return int(isprime(n))
def A052075_gen():
return filter(
lambda p: str(nextprime(p)) in str(p**3), (prime(n) for n in count(1))
)
def A321796_gen():
return filter(
lambda p: str(prevprime(p)) in str(p**3), (prime(n) for n in count(2))
)
def A003136_gen():
return (
n
for n in count(0)
if all(e % 2 == 0 for p, e in factorint(n).items() if p % 3 == 2)
)
def A000045(n):
return fibonacci(n)
def A000045_gen(): # generator of terms
a, b = 0, 1
yield a
while True:
yield b
a, b = b, a + b
def A122045(n):
return euler(n)
@lru_cache(maxsize=None)
def A000219(n):
return (
1
if n == 0
else (
divisor_sigma(n, 2)
+ sum(divisor_sigma(k + 1, 2) * A000219(n - k - 1) for k in range(n - 1))
)
// n
)
def A039834_gen(): # generator of terms
a, b = 1, 1
yield a
while True:
yield b
a, b = b, a - b
def A039834(n):
return fibonacci(-n)
@lru_cache(maxsize=None)
def A001970_helper(n):
return sum(d * npartitions(d) for d in divisors(n, generator=True))
@lru_cache(maxsize=None)
def A001970(n):
return (
1
if n <= 1
else (
A001970_helper(n)
+ A001970_helper(n - 1)
+ sum(A001970_helper(k + 1) * A001970(n - k - 1) for k in range(n - 2))
)
// n
)
def A350858(n):
return (
1
if n == 0
else min(
Matrix(n, n, p).per()
for p in permutations(prime(m) for m in range(1, n**2 + 1))
)
)
def A350859(n):
return (
1
if n == 0
else max(
Matrix(n, n, p).per()
for p in permutations(prime(m) for m in range(1, n**2 + 1))
)
)
def A350565(n):
return (
1
if n == 0
else min(Matrix(n, n, p).per() for p in permutations(range(1, n**2 + 1)))
)
def A350566(n):
return (
1
if n == 0
else max(Matrix(n, n, p).per() for p in permutations(range(1, n**2 + 1)))
)
def A350230_gen(startvalue=1):
return (
n
for n in count(max(startvalue, 1))
if all((isprime(n + d + n // d) for d in divisors(n) if d * d <= n))
)
def A254926(n):
return prod(
p**e - (p ** (e - 3) if e >= 3 else 0) for p, e in factorint(n).items()
)
def A349309_gen(startvalue=1): # generator of terms >= startvalue
a = prod(
p**e - (p ** (e - 3) if e >= 3 else 0)
for p, e in factorint(max(startvalue, 1)).items()
)
for k in count(max(startvalue, 1)):
b = prod(
p**e - (p ** (e - 3) if e >= 3 else 0)
for p, e in factorint(k + 1).items()
)
if a == b:
yield k
a = b
def A350179_gen():
return (
p
for p in (prime(n) for n in count(1))
if max(factorint(p**3 - 1).values()) < 3
)
def A328727_gen(startvalue=0): # generator of terms
for n in count(max(startvalue, 0)):
s = gmpy2digits(n, 3)
for i in range(len(s) - 1):
if "0" not in s[i : i + 2]:
break
else:
yield n
def A350868(n):
if n < 2:
return 2 + n
qlist = [prime(i) - 2 for i in range(2, n + 2)]
p = prime(n + 1)
mlist = [2 * k**2 for k in range(1, n + 1)]
while True:
if qlist == mlist:
return p - mlist[-1]
qlist = [q - qlist[0] for q in qlist[1:]]
r = nextprime(p)
qlist.append(r - p + qlist[-1])
p = r
def A095258_gen(): # generator of terms
bset, s = {1}, 3
yield 1
while True:
for d in divisors(s):
if d not in bset:
yield d
bset.add(d)
s += d
break
def A308751_gen(): # generator of terms
bset, s = {1}, 3
yield 2
while True:
for d in divisors(s):
if d not in bset:
yield s // d
bset.add(d)
s += d
break
def A350741_gen(): # generator of terms
bset, c, s = {1}, 1, 3
yield 1
while True:
for d in divisors(s):
if d not in bset:
if d > c:
yield d
c = d
bset.add(d)
s += d
break
def A253415_gen(): # generator of terms, first term is a(2)
bset, m, s = {1}, 2, 3
while True:
for d in divisors(s):
if d not in bset:
bset.add(d)
while m in bset:
m += 1
yield m
s += d
break
def A253425_gen(): # generator of terms
bset, l, m, s = {1}, 0, 2, 3
while True:
for d in divisors(s):
if d not in bset:
bset.add(d)
if m in bset:
yield l
l = 1
while m in bset:
m += 1
else:
l += 1
s += d
break
def A350701(n):
return 0 if n <= 1 else (lambda x: isqrt(x[0] - 1) - isqrt(x[1]))(fib2(n + 1))
def A350701_gen(): # generator of terms
yield from [0, 0]
a, b = 1, 2
while True:
yield isqrt(b - 1) - isqrt(a)
a, b = b, a + b
def A324151(n):
return 2 * multinomial_coefficients(3, 3 * n)[(n, n, n)] // (n + 1) // (n + 2)
def A066750(n):
return gcd(n, sum(int(d) for d in str(n)))
def A348192_gen(): # generator of terms
blist = [0]
yield 0
for n in count(1):
blist.append(1 + blist[n - gcd(n, sum(int(d) for d in str(n)))])
yield blist[-1]
def A306354(n):
return gcd(n, sum(int(d) ** len(str(n)) for d in str(n)))
def A348591(n):
return (lambda x, y: int(x[0] * x[1] % y))(lucas2(n + 1), fib(n + 2))
def A350932(n):
return min(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).det()
for p in permutations(prime(i) for i in range(1, 2 * n))
)
def A350933(n):
return max(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).det()
for p in permutations(prime(i) for i in range(1, 2 * n))
)
def A350930(n):
return min(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).det()
for p in permutations(range(1, 2 * n))
)
def A350931(n):
return max(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).det()
for p in permutations(range(1, 2 * n))
)
def A350937(n):
return (
1
if n == 0
else min(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).per()
for p in permutations(range(1, 2 * n))
)
)
def A350938(n):
return (
1
if n == 0
else max(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).per()
for p in permutations(range(1, 2 * n))
)
)
def A350939(n):
return (
1
if n == 0
else min(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).per()
for p in permutations(prime(i) for i in range(1, 2 * n))
)
)
def A350940(n):
return (
1
if n == 0
else max(
Matrix([p[n - 1 - i : 2 * n - 1 - i] for i in range(n)]).per()
for p in permutations(prime(i) for i in range(1, 2 * n))
)
)
def A350956(n):
return max(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).det()
for p in permutations(prime(i) for i in range(1, n + 1))
)
def A350955(n):
return min(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).det()
for p in permutations(prime(i) for i in range(1, n + 1))
)
def A350954(n):
return max(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).det()
for p in permutations(range(1, n + 1))
)
def A350953(n):
return min(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).det()
for p in permutations(range(1, n + 1))
)
def A348891(n):
return min(
d
for d in (
abs(Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).det())
for p in permutations(prime(i) for i in range(1, n + 1))
)
if d > 0
)
def A347718(n):
return prod(
(q ** (r + 1) - 1) // (q - 1)
for q, r in sum(
(
Counter(factorint((p ** (n * (e + 1)) - 1) // (p**n - 1)))
for p, e in factorint(n).items()
),
Counter(),
).items()
)
def A064165(n):
return prod(
r + 1
for q, r in sum(
(
Counter(factorint((p ** (n * (e + 1)) - 1) // (p**n - 1)))
for p, e in factorint(n).items()
),
Counter(),
).items()
)
def A351021(n):
return (
1
if n == 0
else min(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).per()
for p in permutations(prime(i) for i in range(1, n + 1))
)
)
def A351022(n):
return (
1
if n == 0
else max(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).per()
for p in permutations(prime(i) for i in range(1, n + 1))
)
)
def A351020(n):
return (
1
if n == 0
else max(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).per()
for p in permutations(range(1, n + 1))
)
)
def A351019(n):
return (
1
if n == 0
else min(
Matrix([p[i:0:-1] + p[0 : n - i] for i in range(n)]).per()
for p in permutations(range(1, n + 1))
)
)
def A351114(n):
f = factorint(n)
return int(
not prod(p * (p ** (e + 1) - 1) for p, e in f.items())
% (n * prod((p - 1) ** 2 for p in f))
)
def A005230_gen(): # generator of terms
blist = [1]
for n in count(1):
yield blist[-1]
blist.append(sum(blist[-i] for i in range(1, (isqrt(8 * n) + 3) // 2)))
def A002024(n):
return (isqrt(8 * n) + 1) // 2
def A005130(n):
return prod(factorial(3 * k + 1) for k in range(n)) // prod(
factorial(n + k) for k in range(n)
)
def A049503(n):
return (
prod(factorial(3 * k + 1) for k in range(n))
// prod(factorial(n + k) for k in range(n))
) ** 2
def A000140(n):
return (
1
if n == 1
else max(
Poly(
prod(sum(symbolx**i for i in range(j + 1)) for j in range(n))
).all_coeffs()
)
)
def A000055(n):
return (
1
if n == 0
else A000081(n)
- sum(A000081(i) * A000081(n - i) for i in range(1, n // 2 + 1))
+ (0 if n % 2 else (A000081(n // 2) + 1) * A000081(n // 2) // 2)
)
def A217420(n):
return sum(A000081(i) * A000081(n - 1 - i) for i in range(1, (n - 1) // 2 + 1)) - (
(A000081((n - 1) // 2) + 1) * A000081((n - 1) // 2) // 2 if n % 2 else 0
)
def A336039_gen(startvalue=1):
return (k for k in count(max(startvalue, 1)) if not A000081(k) % k)
def A036361(n):
return int(n * (n - 1) * (2 * n - 3) ** (n - 4) // 2)
def A036506(n):
return int(n * (n - 3) * (n - 2) * (n - 1) * (4 * n - 15) ** (n - 6) // 24)
def A036362(n):
return int(n * (n - 2) * (n - 1) * (3 * n - 8) ** (n - 5) // 6)
def A000051(n):
return 2**n + 1
def A145071(n):
return 2 ** (n + 1) + n - 2
def A060477(n):
return sum(mobius(n // d) * (2**d + 1) for d in divisors(n, generator=True)) // n
def A001037(n):
return (
1
if n == 0
else sum(mobius(n // d) * 2**d for d in divisors(n, generator=True)) // n
)
def A027375(n):
return sum(mobius(n // d) * 2**d for d in divisors(n, generator=True))
def A000740(n):
return sum(mobius(n // d) * 2 ** (d - 1) for d in divisors(n, generator=True))
def A059966(n):
return sum(mobius(n // d) * (2**d - 1) for d in divisors(n, generator=True)) // n
def A343318(n):
return (2**n + 1) ** 3
def A333474_gen(startvalue=0): # generator of terms
m = 2 ** (s := max(startvalue, 0))
n = m + 1
for k in count(s):
if not n % sum(int(d) for d in str(n)):
yield k
m *= 2
n = m + 1
def A023578(n):
return min((p for p in factorint(prime(n) + 3) if p > 2), default=1)
def A078701(n):
return min((p for p in factorint(n) if p > 2), default=1)
@lru_cache(maxsize=None)
def A008472(n):
return sum(primefactors(n))
@lru_cache(maxsize=None)
def A000607(n):
return (
1 if n == 0 else sum(A008472(k) * A000607(n - k) for k in range(1, n + 1)) // n
)
def A007778(n):
return n ** (n + 1)
def A007830(n):
return (n + 3) ** n
def A008785(n):
return (n + 4) ** n
def A008786(n):
return (n + 5) ** n
def A008787(n):
return (n + 6) ** n
def A008788(n):
return n ** (n + 2)
def A008789(n):
return n ** (n + 3)
def A008790(n):
return n ** (n + 4)
def A008791(n):
return n ** (n + 5)
def A000169(n):
return n ** (n - 1)
def A329723(n):
return 1 if n <= 1 else lucas(n - 2)
def A278159(n):
return RLT(n, primorial)
def A246674(n):
return RLT(n, lambda m: 2**m - 1)
def A001317(n):
return int("".join(str(int(not (~n & k))) for k in range(n + 1)), 2)
def A247282(n):
return RLT(
n, lambda m: int("".join(str(int(not (~(m - 1) & k))) for k in range(m)), 2)
)
def A286575(n):
return RLT(n, lambda m: 2 ** (bin(m).count("1")))
def A286574(n):
return len(bin(RLT(n, lambda m: 2 ** (bin(m).count("1"))))) - 3
def A246685(n):
return RLT(n, lambda m: 1 if m <= 1 else 2 ** (2 ** (m - 2)) + 1)
def A000012(n):
return 1
def A000007(n):
return int(n == 0)
def A046523(n):
return prod(
prime(i + 1) ** e
for i, e in enumerate(sorted(factorint(n).values(), reverse=True))
)
def A056040(n):
return factorial(n) // factorial(n // 2) ** 2
def A246661(n):
return RLT(n, lambda m: factorial(m) // factorial(m // 2) ** 2)
def A245564(n):
return RLT(n, lambda m: fibonacci(m + 2))
def A185017(n):
return int(n == 7)
def A185016(n):
return int(n == 6)
def A185015(n):
return int(n == 5)
def A185014(n):
return int(n == 4)
def A185013(n):
return int(n == 3)
def A185012(n):
return int(n == 2)
def A063524(n):
return int(n == 1)
def A014081(n):
return sum(len(d) - 1 for d in split("0+", bin(n)[2:]) if d != "")
def A053645(n):
return 0 if n <= 1 else int(bin(n)[3:], 2)
@lru_cache(maxsize=None)
def A346422(n):
return (
1
if n <= 1
else A346422(int((s := bin(n)[2:])[1:], 2))
* (1 + sum(len(d) - 1 for d in split("0+", s) if d != ""))
)
def A245195(n):
return 2 ** A014081(n)
def A245565(n):
return RLT(n, lambda m: next(islice(A000129_gen(), m + 1, None)))
def A329722(n):
return RLT(n, lambda m: 1 if m <= 1 else lucas(m - 2))
def A278161(n):
return RLT(n, lambda m: m // 2 + 1)
def A000930_gen(): # generator of terms
blist = [1] * 3
while True:
yield blist[0]
blist = blist[1:] + [blist[0] + blist[2]]
def A329720(n):
return RLT(n, lambda m: next(islice(A000930_gen(), m, None)))
def A106737(n):
return RLT(n, lambda m: m + 1)
def A277561(n):
return RLT(n, lambda m: 1 if m == 0 else 2)
def A246028(n):
return RLT(n, lambda m: fibonacci(m + 1))
def A001316(n):
return 2 ** A000120(n)
def A102376(n):
return 4 ** A000120(n)
def A036044(n):
return -int((s := bin(n)[-1:1:-1]), 2) - 1 + 2 ** len(s)
def A059894(n):
return n if n <= 1 else -int((s := bin(n)[-1:2:-1]), 2) - 1 + 2 ** (len(s) + 1)
def A284799(n):
return -int((s := gmpy2digits(n, 4)[::-1]), 4) - 1 + 4 ** len(s)
def A284797(n):
return -int((s := gmpy2digits(n, 3)[::-1]), 3) - 1 + 3 ** len(s)
def A284798_gen():
return (
n
for n in count(0)
if not n + int((s := gmpy2digits(n, 3)[::-1]), 3) + 1 - 3 ** len(s)
)
def A159006(n):
return -int((s := bin(prime(n))[-1:1:-1]), 2) - 1 + 2 ** len(s)
def A284807(n):
return -int((s := oct(n)[-1:1:-1]), 8) - 1 + 8 ** len(s)
def A351198(n):
return sum(p**10 for p in primefactors(n))
def A351197(n):
return sum(p**9 for p in primefactors(n))
def A351196(n):
return sum(p**8 for p in primefactors(n))
def A351262(n):
return sum((n // p) ** 10 for p in primefactors(n))
def A351249(n):
return sum((n // p) ** 9 for p in primefactors(n))
def A351248(n):
return sum((n // p) ** 8 for p in primefactors(n))
def A069359(n):
return sum(n // p for p in primefactors(n))
def A351219(n):
return prod(fibonacci(e + 1) for e in factorint(n).values())
def A002371(n):
return 0 if n == 1 or n == 3 else n_order(10, prime(n))
def A007732(n):
return n_order(10, n // 2 ** multiplicity(2, n) // 5 ** multiplicity(5, n))
def A350814_gen(startvalue=1):
return filter(
lambda m: max(repeating_decimals_expr(Fraction(1, m), digits_only=True)) == "3",
count(max(startvalue, 1)),
)
def A072982_gen():
return (
p
for p in (prime(n) for n in count(2))
if p != 5 and bin(n_order(10, p))[2:].rstrip("0") == "1"
)
def A051628(n):
return max(multiplicity(2, n), multiplicity(5, n))
def A341383_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if (
max(str(10 ** (max(m2, m5) + n_order(10, m // 2**m2 // 5**m5)) // m))
== "2"
):
yield m
def A333236(n):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
return int(
max(str(10 ** (max(m2, m5) + n_order(10, n // 2**m2 // 5**m5)) // n))
)
def A333442(n):
if n == 1:
return 0
m2, m5 = multiplicity(2, n), multiplicity(5, n)
r = max(m2, m5) + n_order(10, n // 2**m2 // 5**m5)
s = str(10**r // n).zfill(r)
return s.index(max(s)) + 1
def A333237_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if (
max(str(10 ** (max(m2, m5) + n_order(10, m // 2**m2 // 5**m5)) // m))
== "9"
):
yield m
def A351355(n):
return (
0
if n == 1
else n * n
- sum(2 * n // k for k in range(2, 2 * n))
+ sum(n // k for k in range(2, n))
)
def A351362(n):
return (
1
if n == 2
else n * n
- 1
- sum((2 * n - 1) // k for k in range(2, 2 * n - 1))
+ sum((n - 1) // k for k in range(2, n - 1))
)
def A351139(n):
if n == 2:
return 14
for r in count(1):
if (
k := continued_fraction_reduce(
[r, list(range(1, n + 1)) + list(range(n - 1, 0, -1)) + [2 * r]]
)
** 2
).is_integer:
return k
def A350562_gen(): # generator of terms
bdict = {1: 1}
yield 1
b = 0
for n in count(3):
yield b
c = (n - bdict[b]) * b if b in bdict else 1
bdict[b], b = n - 1, c
def A350574_gen(): # generator of terms
for l in count(1):
rlist = []
for a in combinations_with_replacement("123456789", l):
s = "".join(a)
p, q = int(s), int(s[::-1])
if p != q and isprime(p) and isprime(q):
for b in multiset_permutations(a):
r = int("".join(b))
if p < r < q and isprime(r):
rlist.append(r)
break
yield from sorted(rlist)
def A075188(n):
m = lcm(*range(1, n + 1))
mlist = tuple(m // i for i in range(1, n + 1))
k = sum(mlist)
c = 0
for l in range(0, n // 2 + 1):
for p in combinations(mlist, l):
s = sum(p)
r, t = s // gcd(s, m), (k - s) // gcd(k - s, m)
if isprime(r):
if 2 * l != n:
c += 1
if isprime(t):
c += 1
return c
def A351470_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if (
max(str(10 ** (max(m2, m5) + n_order(10, m // 2**m2 // 5**m5)) // m))
== "4"
):
yield m
def A351471_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if (
max(str(10 ** (max(m2, m5) + n_order(10, m // 2**m2 // 5**m5)) // m))
== "5"
):
yield m
def A351472_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if (
max(str(10 ** (max(m2, m5) + n_order(10, m // 2**m2 // 5**m5)) // m))
== "6"
):
yield m
def A075226(n):
m = lcm(*range(1, n + 1))
c, mlist = 0, tuple(m // i for i in range(1, n + 1))
for l in range(n, -1, -1):
if sum(mlist[:l]) < c:
break
for p in combinations(mlist, l):
s = sum(p)
s //= gcd(s, m)
if s > c and isprime(s):
c = s
return c
def A256221(n):
m = lcm(*range(1, n + 1))
fset, fibset, mlist = set(), set(), tuple(m // i for i in range(1, n + 1))
a, b, k = 0, 1, sum(mlist)
while b <= k:
fibset.add(b)
a, b = b, a + b
for l in range(1, n // 2 + 1):
for p in combinations(mlist, l):
s = sum(p)
if (t := s // gcd(s, m)) in fibset:
fset.add(t)
if 2 * l != n and (t := (k - s) // gcd(k - s, m)) in fibset:
fset.add(t)
if (t := k // gcd(k, m)) in fibset:
fset.add(t)
return len(fset)
def A256220(n):
m = lcm(*range(1, n + 1))
fibset, mlist = set(), tuple(m // i for i in range(1, n + 1))
a, b, c, k = 0, 1, 0, sum(mlist)
while b <= k:
fibset.add(b)
a, b = b, a + b
for l in range(1, n // 2 + 1):
for p in combinations(mlist, l):
s = sum(p)
if s // gcd(s, m) in fibset:
c += 1
if 2 * l != n and (k - s) // gcd(k - s, m) in fibset:
c += 1
return c + int(k // gcd(k, m) in fibset)
def A351532(n):
return sum(
1
for d in diop_quadratic(
n**2 + 3 * symbolx * symboly - 2 * n * (symbolx + symboly)
)
if 0 < d[0] < n and 0 < d[1] < n
)
def A241883(n):
c, w = 0, n + 1
while 6 * n + w * (22 * n + w * (18 * n + w * (4 * n - w - 6) - 11) - 6) >= 0:
x = max(w + 1, n * w // (w - n) + 1)
wx = w * x
while (
2 * n * w
+ x
* (2 * n + w * (6 * n - 2) + x * (3 * n + w * (3 * n - 3) + x * (n - w)))
>= 0
):
y = max(x + 1, w * x * n // (x * (w - n) - w * n) + 1)
wxy = wx * y
while (
x * (n * w + y * (n + w * (2 * n - 1) + y * (n - w)))
+ y * (n * w * y + n * w)
>= 0
):
z, r = divmod(n * wxy, wxy - n * (x * y + w * (x + y)))
if z > y and r == 0:
c += 1
y += 1
wxy += wx
x += 1
wx += w
w += 1
return c
def A347569(n):
c, p = 0, n + 1
while (
120 * n
+ p
* (
548 * n
+ p
* (
675 * n
+ p * (340 * n + p * (75 * n + p * (6 * n - p - 15) - 85) - 225)
- 274
)
- 120
)
>= 0
):
q = max(p + 1, n * p // (p - n) + 1)
pq = p * q
while (
p
* (
24 * n
+ q
* (
100 * n
+ q * (105 * n + q * (40 * n + q * (5 * n - q - 10) - 35) - 50)
- 24
)
)
+ q * (24 * n + q * (50 * n + q * (35 * n + q * (n * q + 10 * n))))
>= 0
):
r = max(q + 1, n * pq // (pq - n * (p + q)) + 1)
pqr = pq * r
while (
p
* (
q
* (
6 * n
+ r * (22 * n + r * (18 * n + r * (4 * n - r - 6) - 11) - 6)
)
+ r * (6 * n + r * (11 * n + r * (n * r + 6 * n)))
)
+ q * r * (6 * n + r * (11 * n + r * (n * r + 6 * n)))
>= 0
):
s = max(r + 1, n * pqr // (pqr - n * (pq + r * (p + q))) + 1)
pqrs = pqr * s
while (
p
* (
q
* (
r * (2 * n + s * (6 * n + s * (3 * n - s - 3) - 2))
+ s * (2 * n + s * (n * s + 3 * n))
)
+ r * s * (2 * n + s * (n * s + 3 * n))
)
+ q * r * s * (2 * n + s * (n * s + 3 * n))
>= 0
):
t = max(
s + 1,
n * pqrs // (pqrs - n * (pqr + pq * s + r * s * (p + q))) + 1,
)
pqrst = pqrs * t
while (
p
* (
q
* (
r * (s * (n + t * (2 * n - t - 1)) + t * (n * t + n))
+ s * t * (n * t + n)
)
+ r * s * t * (n * t + n)
)
+ q * r * s * t * (n * t + n)
>= 0
):
u, z = divmod(
n * pqrst,
pqrst
- n
* (
q * r * s * t
+ p * r * s * t
+ pq * s * t
+ pqr * t
+ pqrs
),
)
if u > t and z == 0:
c += 1
t += 1
pqrst += pqrs
s += 1
pqrs += pqr
r += 1
pqr += pq
q += 1
pq += p
p += 1
return c
def A351372_gen(): # generator of terms
for z in count(1):
z2 = z**2
for y in range(1, z + 1):
a = isqrt(
d := 3 * y**2 * (12 * z2 - 4 * z - 1)
- 3 * z2 * (4 * y + 1)
- 2 * y * z
)
if a**2 == d:
x, r = divmod(12 * y * z - 2 * y - 2 * z - 2 * a, 4)
if y <= x <= z and r == 0:
yield from (y, x, z)
def A351528_gen(): # generator of terms
yield from (
int(d[::-1], 2)
for l in count(1)
for d in sorted(bin(m)[:1:-1] for m in primerange(2 ** (l - 1), 2**l))
)
def A104154_gen(): # generator of terms
yield from (
int(d[::-1])
for l in count(1)
for d in sorted(str(m)[::-1] for m in primerange(10 ** (l - 1), 10**l))
)
def A098957(n):
return int(bin(prime(n))[:1:-1], 2)
def A030101(n):
return int(bin(n)[:1:-1], 2)
def A351105(n):
return (
n
* (
n
* (
n
* (
n
* (
n * (n * (n * (n * (280 * n + 2772) + 10518) + 18711) + 14385)
+ 1323
)
- 2863
)
- 126
)
+ 360
)
// 45360
)
def A347107(n):
return (
n
* (n**2 * (n * (n * (n * (n * (21 * n + 36) - 42) - 84) + 21) + 56) - 8)
// 672
)
def A346642(n):
return (
n
* (n**2 * (n * (n * (n * (n * (21 * n + 132) + 294) + 252) + 21) - 56) + 8)
// 672
)
def A333402_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
k = 1
while k <= m:
k *= 10
rset = {0}
while True:
k, r = divmod(k, m)
if max(str(k)) > "1":
break
else:
if r in rset:
yield m
break
rset.add(r)
k = r
while k <= m:
k *= 10
def A030302_gen(): # generator of terms
return (int(d) for n in count(1) for d in bin(n)[2:])
def A351753(n):
s1, s2 = tuple(), tuple()
for i, s in enumerate(int(d) for n in count(1) for d in bin(n)[2:]):
if i < n:
s1 += (s,)
s2 += (s,)
else:
s2 = s2[1:] + (s,)
if s1 == s2:
return i - n + 2
def A030303_gen(): # generator of terms
return (
i + 1 for i, s in enumerate(d for n in count(1) for d in bin(n)[2:]) if s == "1"
)
def A003607_gen(): # generator of terms
return (
i for i, s in enumerate(d for n in count(0) for d in bin(n)[2:]) if s == "0"
)
def A194472_gen(startvalue=1): # generator of terms
return (
n
for n in count(max(startvalue, 1))
if any(s == n for s in accumulate(divisors(n)[:-2]))
)
def A138591(n):
return len(bin(n + len(bin(n)) - 3)) + n - 3
def A094683(n):
return isqrt(n**3 if n % 2 else n)
def A093112(n):
return (2**n - 1) ** 2 - 2
def A088054_gen(): # generator of terms
f = 1
for k in count(1):
f *= k
if isprime(f - 1):
yield f - 1
if isprime(f + 1):
yield f + 1
def A046760_gen(): # generator of terms
return (
n
for n in count(1)
if len(str(n))
< sum(
len(str(p)) + (len(str(e)) if e > 1 else 0) for p, e in factorint(n).items()
)
)
def A046758_gen(): # generator of terms
return (
n
for n in count(1)
if n == 1
or len(str(n))
== sum(
len(str(p)) + (len(str(e)) if e > 1 else 0) for p, e in factorint(n).items()
)
)
def A034897_gen(): # generator of terms
return (
n
for n in count(2)
if not isprime(n) and (n - 1) % (divisor_sigma(n) - n - 1) == 0
)
def A019279_gen(): # generator of terms
return (n for n in count(1) if divisor_sigma(divisor_sigma(n)) == 2 * n)
def A014080_gen(): # generator of terms
return (
n
for n in count(1)
if sum((1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880)[int(d)] for d in str(n))
== n
)
def A007588(n):
return n * (2 * n**2 - 1)
def A342162(n):
s1, s2, m = tuple(int(d) for d in str(n)), tuple(), -1
l = len(s1)
for i, s in enumerate(int(d) for k in count(0) for d in str(k)):
s2 = (s2 + (s,))[-l:]
if s2 == s1:
if m >= 0:
return i - m
m = i
def A337227(n):
s1 = tuple(int(d) for d in str(n))
s2 = s1
for i, s in enumerate(int(d) for k in count(n + 1) for d in str(k)):
s2 = s2[1:] + (s,)
if s2 == s1:
return i + 1
def A052486_gen(startvalue=1): # generator of terms
return (
n
for n in count(max(startvalue, 1))
if (lambda x: all(e > 1 for e in x) and gcd(*x) == 1)(factorint(n).values())
)
def A007850_gen(startvalue=2): # generator of terms
return filter(
lambda x: not isprime(x)
and all((x // p - 1) % p == 0 for p in primefactors(x)),
count(max(startvalue, 2)),
)
def A334409_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
ds = divisors(n)
if any(
s == 2 * n
for s in accumulate(ds[i] + ds[-1 - i] for i in range((len(ds) - 1) // 2))
):
yield n
def A334410_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
ds = divisors(n)
s = sum(ds)
if s % 2 == 0 and any(2 * a == s for a in accumulate(ds)):
yield n
@lru_cache(maxsize=None)
def A350661(n):
return 1 if n == 1 else A350661(prod(primefactors(n)) - 1) + n
def A351412(n):
if n == 1:
return 1
q, r = divmod(n, 4)
if r == 0:
return n - q + 1
elif r == 2:
return n - q
elif r == 1:
return n + 2 * q - 1
else:
return n + 2 * q
def A106303(n):
a = b = (0,) * 4 + (1 % n,)
s = 1 % n
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % n
if a == b:
return m
def A106304(n):
a = b = (0,) * 4 + (1 % (p := prime(n)),)
s = 1 % p
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % p
if a == b:
return m
def A193994(n):
a = b = (0,) * 4 + (1 % n,)
c, s = 0, 1 % n
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % n
c += int(s == 0)
if a == b:
return c
def A106295(n):
a = b = (4 % n, 1 % n, 3 % n, 7 % n)
s = sum(b) % n
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % n
if a == b:
return m
def A106297(n):
a = b = (5 % n, 1 % n, 7 % n, 3 % n, 15 % n)
s = sum(b) % n
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % n
if a == b:
return m
def A106298(n):
a = b = (5 % (p := prime(n)), 1 % p, 7 % p, 3 % p, 15 % p)
s = sum(b) % p
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % p
if a == b:
return m
def A068527(n):
return 0 if n == 0 else (isqrt(n - 1) + 1) ** 2 - n
def A348596(n):
return (isqrt(2 * n) + 1) ** 2 - 2 * n - 1
def A350962(n):
return 0 if n == 0 else (isqrt(2 * n - 1) + 1) ** 2 - 2 * n
def A106290(n):
bset, tset = set(), set()
for t in product(range(n), repeat=5):
t2 = t
for c in count(1):
t2 = t2[1:] + (sum(t2) % n,)
if t == t2:
bset.add(c)
tset.add(t)
break
if t2 in tset:
tset.add(t)
break
return len(bset)
def A351657_helper(n, pe):
a = b = (0,) * (n - 1) + (1 % pe,)
s = 1 % pe
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % pe
if a == b:
return m
def A351657(n):
return (
1
if n == 1
else lcm(*(A351657_helper(n, p**e) for p, e in factorint(n).items()))
)
def A143293_gen():
return accumulate(accumulate(chain((1,), (prime(n) for n in count(1))), mul))
def A225727_gen():
return (
i + 1
for i, m in enumerate(
accumulate(accumulate(chain((1,), (prime(n) for n in count(1))), mul))
)
if m % (i + 1) == 0
)
def A225841_gen():
return (
i + 1
for i, m in enumerate(accumulate(accumulate((prime(n) for n in count(1)), mul)))
if m % (i + 1) == 0
)
def A225728_gen():
return (
prime(i + 1)
for i, m in enumerate(
accumulate(accumulate(chain((1,), (prime(n) for n in count(1))), mul))
)
if m % prime(i + 1) == 0
)
def A045345_gen():
return (
i + 1
for i, m in enumerate(accumulate(prime(n) for n in count(1)))
if m % (i + 1) == 0
)
def A007504_gen():
return accumulate(prime(n) if n > 0 else 0 for n in count(0))
@lru_cache(maxsize=None)
def A351889_T(n, k): # computes the period of the n-step Fibonacci sequence mod k
if len(fs := factorint(k)) <= 1:
a = b = (0,) * (n - 1) + (1 % k,)
s = 1 % k
for m in count(1):
b, s = b[1:] + (s,), (s + s - b[0]) % k
if a == b:
return m
else:
return lcm(*(A351889_T(n, p**e) for p, e in fs.items()))
def A351568(n):
return prod(
1 if e % 2 else (p ** (e + 1) - 1) // (p - 1) for p, e in factorint(n).items()
)
def A351569(n):
return prod(
(p ** (e + 1) - 1) // (p - 1) if e % 2 else 1 for p, e in factorint(n).items()
)
def A350389(n):
return prod(p**e if e % 2 else 1 for p, e in factorint(n).items())
def A351808_gen(): # generator of terms
return (
q
for q, r in (
divmod(prod(int(d) for d in str(m**2)), prod(int(d) for d in str(m)))
for m in count(1)
if "0" not in str(m)
)
if r == 0
)
def A351807_gen(): # generator of terms
return (
m
for m in count(1)
if "0" not in str(m)
and prod(int(d) for d in str(m**2)) % prod(int(d) for d in str(m)) == 0
)
def A046738(n):
a = b = (0, 0, 1 % n)
for m in count(1):
b = b[1:] + (sum(b) % n,)
if a == b:
return m
def A106302(n):
a = b = (0,) * 2 + (1 % (p := prime(n)),)
for m in count(1):
b = b[1:] + (sum(b) % p,)
if a == b:
return m
def A195199(n):
f = Counter(factorint(n))
d = prod(e + 1 for e in f.values())
for m in count(2):
if prod(e + 1 for e in (f + Counter(factorint(m))).values()) > 2 * d:
return m * n
def A351126(n):
f = Counter(factorint(n))
d = prod(e + 1 for e in f.values())
for m in count(2):
if prod(e + 1 for e in (f + Counter(factorint(m))).values()) > 2 * d:
return m
def A037276(n):
return (
1
if n == 1
else int("".join(str(d) for d in sorted(factorint(n, multiple=True))))
)
def A351975_gen(startvalue=1): # generator of terms
for k in count(max(startvalue, 1)):
c = 0
for d in sorted(factorint(k, multiple=True)):
c = (c * 10 ** len(str(d)) + d) % k
if c == k - 1:
yield k
def A349705_gen(startvalue=1): # generator of terms
for k in count(max(startvalue, 1)):
c = 0
for d in sorted(factorint(k, multiple=True)):
c = (c * 10 ** len(str(d)) + d) % k
if c == 1:
yield k
def A347859(n):
return (
n // 2
if n % 2 == 0 and isprime(n // 2)
else 3 * (n - 1) // 2
if n % 2 and isprime((n - 1) // 2)
else n
)
def A340592(n):
c = 0
for d in sorted(factorint(n, multiple=True)):
c = (c * 10 ** len(str(d)) + d) % n
return c
def A001178(n):
m = n
for c in count(0):
k = A001175(m)
if k == m:
return c
m = k
def A351989(n):
return fibonacci((p := prime(n)) - jacobi_symbol(p, 5)) % p**3
def A352038(n):
return prod(
(p ** (10 * (e + 1)) - 1) // (p**10 - 1)
for p, e in factorint(n).items()
if p > 2
) - (n**10 if n % 2 else 0)
def A352047(n):
return (
prod(
p**e if p == 2 else (p ** (e + 1) - 1) // (p - 1)
for p, e in factorint(n).items()
)
- n % 2
)
def A351619(n):
return (0 if n % 2 else 2) - len(primefactors(n))
def A352023_gen(): # generator of terms
yield from (2, 3, 5)
p = 7
while True:
if "9" not in str(10 ** (n_order(10, p)) // p):
yield p
p = nextprime(p)
def A187614_gen(): # generator of terms
yield from (2, 3, 5)
p = 7
while True:
if len(set("0" + str(10 ** (n_order(10, p)) // p))) < 10:
yield p
p = nextprime(p)
def A216664_gen(startvalue=1): # generator of terms
for n in count(max(startvalue + 1 - startvalue % 2, 1), 2):
if 10 ** ((n + 1) // 2) // n % 10 == 9:
yield n
def A351782(n):
return n - 1 - int(n % 4 == 0)
def A050795_gen(startvalue=2): # generator of terms
for k in count(max(startvalue, 2)):
if all(
map(lambda d: d[0] % 4 != 3 or d[1] % 2 == 0, factorint(k**2 - 1).items())
):
yield k
def A140612_gen(startvalue=0): # generator of terms
for k in count(max(startvalue, 0)):
if all(
starmap(
lambda d, e: e % 2 == 0 or d % 4 != 3, factorint(k * (k + 1)).items()
)
):
yield k
def A351211(n):
return integer_nthroot(3 * 10 ** (14 * (n - 1)), 14)[0] % 10
def A351210(n):
return integer_nthroot(3 * 10 ** (13 * (n - 1)), 13)[0] % 10
def A351209(n):
return integer_nthroot(3 * 10 ** (12 * (n - 1)), 12)[0] % 10
def A351208(n):
return integer_nthroot(3 * 10 ** (11 * (n - 1)), 11)[0] % 10
def A246711(n):
return integer_nthroot(3 * 10 ** (10 * (n - 1)), 10)[0] % 10
def A011273(n):
return integer_nthroot(9 * 10 ** (19 * (n - 1)), 19)[0] % 10
def A352152(n):
return int(
"".join(
"".join(list(g) if k else list(g)[::-1])
for k, g in groupby(str(n), key=lambda x: x == "0")
)
)
@lru_cache(maxsize=None)
def A006165(n):
return 1 if n <= 2 else A006165(n // 2) + A006165((n + 1) // 2)
@lru_cache(maxsize=None)
def A060973(n):
return n - 1 if n <= 2 else A060973(n // 2) + A060973((n + 1) // 2)
@lru_cache(maxsize=None)
def A283187(n):
return (
n
if n <= 1
else A283187(n // 2) + (-1 if A283187((n + 1) // 2) % 2 else 1)
if n % 2
else 2 * A283187(n // 2)
)
@lru_cache(maxsize=None)
def A087808(n):
return 0 if n == 0 else A087808(n // 2) + (1 if n % 2 else A087808(n // 2))
def A352179_gen(startvalue=1): # generator of terms
k = max(startvalue, 1)
k14 = 14**k
while True:
if str(k14)[:2] == "14":
yield k
k += 1
k14 *= 14
def A352239_gen(): # generator of terms
for l in count(0):
k14 = 14 ** (14 * 10**l)
for k in range(14 * 10**l, 15 * 10**l):
if str(k14)[:2] == "14":
yield k
k14 *= 14
def A053646(n):
return min(n - (m := 2 ** (len(bin(n)) - 3)), 2 * m - n)
def A350809(n):
return len(set(p - n % p for p in primerange(2, n + 1)))
def A352232(n):
return (2 ** n_order(2, p := prime(n)) - 1) // p
def A351985(n):
return abs(sum((-1 if a % 2 else 1) * int(b) ** 3 for a, b in enumerate(str(n))))
def A352296(n):
if n == 0:
return 1
pset, plist, pmax = {2}, [2], 4
for m in count(2):
if m > pmax:
plist.append(nextprime(plist[-1]))
pset.add(plist[-1])
pmax = plist[-1] + 2
c = 0
for p in plist:
if 2 * p > m:
break
if m - p in pset:
c += 1
if c == n:
return m
def A014494(n):
return (2 * n + 1) * (n + n % 2)
def A352115(n):
return (n + 1) * (2 * n * (n + 2) + 3 * (n % 2)) // 3
def A351653(n):
return int("".join(str(len(list(g))) for k, g in groupby(str(n))))
def A318927(n):
return int("".join(str(len(list(g))) for k, g in groupby(bin(n)[2:])))
def A318926(n):
return int("".join(str(len(list(g))) for k, g in groupby(bin(n)[:1:-1])))
def A352187_gen(): # generator of terms
bset, blist, mmax = {1, 2}, [1, 2], 3
yield from blist
while True:
for m in count(mmax):
if gcd(m, blist[-1]) > 1 and m not in bset:
if (
all(blist[-2] % p == 0 for p in primefactors(blist[-1]))
or gcd(m, blist[-2]) == 1
):
yield m
blist = [blist[-1], m]
bset.add(m)
while mmax in bset:
mmax += 1
break
def A352191_gen(): # generator of terms
bset, blist, mmax, c = {1, 2}, [1, 2], 3, 2
yield from blist
while True:
for m in count(mmax):
if gcd(m, blist[-1]) > 1 and m not in bset:
if (
all(blist[-2] % p == 0 for p in primefactors(blist[-1]))
or gcd(m, blist[-2]) == 1
):
if m > c:
yield m
c = m
blist = [blist[-1], m]
bset.add(m)
while mmax in bset:
mmax += 1
break
def A352192_gen(): # generator of terms
bset, blist, mmax, c = {1, 2}, [1, 2], 3, 2
yield from blist
for n in count(3):
for m in count(mmax):
if gcd(m, blist[-1]) > 1 and m not in bset:
if (
all(blist[-2] % p == 0 for p in primefactors(blist[-1]))
or gcd(m, blist[-2]) == 1
):
if m > c:
yield n
c = m
blist = [blist[-1], m]
bset.add(m)
while mmax in bset:
mmax += 1
break
def A055085(n): # assumes n <= 62
dlist = tuple(gmpy2digits(d, n) for d in range(n))
for l in count(n - 1):
for t in product(dlist, repeat=l - n + 1):
for d in range(1, n):
for u in multiset_permutations(sorted(t + dlist[:d] + dlist[d + 1 :])):
m = mpz("".join((dlist[d],) + tuple(u)), n)
for b in range(n - 1, 1, -1):
if len(set(gmpy2digits(m, b))) < b:
break
else:
return int(m)
def A351426(n): # assumes n <= 62
if n == 2:
return 1
dlist = tuple(gmpy2digits(d, n) for d in range(n))
for l in count(n - 2):
for d in range(1, n):
c = None
for t in product(dlist, repeat=l - n + 2):
for u in multiset_permutations(sorted(t + dlist[1:d] + dlist[d + 1 :])):
m = mpz("".join((dlist[d],) + tuple(u)), n)
for b in range(n - 1, 1, -1):
if len(set(gmpy2digits(m, b)) | {"0"}) < b:
break
else:
if c != None:
c = min(m, c)
else:
c = m
if c != None:
return int(c)
def A352447_gen(): # generator of terms
yield 1
a = Counter()
for k in count(2):
b = Counter(factorint(k - 1))
if all(b[p] <= a[p] for p in b):
yield k
a += b
def A352142_gen(startvalue=1): # generator of terms
return filter(
lambda k: all(
map(lambda x: x[1] % 2 and primepi(x[0]) % 2, factorint(k).items())
),
count(max(startvalue, 1)),
)
def A352141_gen(startvalue=1): # generator of terms
return filter(
lambda k: all(
map(lambda x: not (x[1] % 2 or primepi(x[0]) % 2), factorint(k).items())
),
count(max(startvalue, 1)),
)
@lru_cache(maxsize=None)
def A109129(n):
if n <= 2:
return n - 1
if isprime(n):
return A109129(primepi(n))
return sum(e * A109129(p) for p, e in factorint(n).items())
@lru_cache(maxsize=None)
def A061775(n):
if n == 1:
return 1
if isprime(n):
return 1 + A061775(primepi(n))
return 1 + sum(e * (A061775(p) - 1) for p, e in factorint(n).items())
@lru_cache(maxsize=None)
def A196050(n):
if n == 1:
return 0
if isprime(n):
return 1 + A196050(primepi(n))
return sum(e * A196050(p) for p, e in factorint(n).items())
@lru_cache(maxsize=None)
def A109082(n):
if n == 1:
return 0
if isprime(n):
return 1 + A109082(primepi(n))
return max(A109082(p) for p in primefactors(n))
def A351928(n):
kmax, m = 3**n, (3 ** (n - 1)).bit_length()
k2 = pow(2, m, kmax)
for k in count(m):
a = k2
while a > 0:
a, b = divmod(a, 3)
if b == 2:
break
else:
return k
k2 = 2 * k2 % kmax
def A351927(n):
kmax, m = 3**n, (3 ** (n - 1)).bit_length()
k2 = pow(2, m, kmax)
for k in count(m):
a = k2
if 3 * a >= kmax:
while a > 0:
a, b = divmod(a, 3)
if b == 0:
break
else:
return k
k2 = 2 * k2 % kmax
def A030298_gen(): # generator of terms
return chain.from_iterable(p for l in count(2) for p in permutations(range(1, l)))
def A061077(n):
return sum(prod(int(d) for d in str(2 * i + 1)) for i in range(n))
def A061078(n):
return sum(prod(int(d) for d in str(2 * i + 2)) for i in range(n))
def A061076(n):
return sum(prod(int(d) for d in str(i)) for i in range(1, n + 1))
def A352329_gen(): # generator of terms
for l in count(1):
if (r := l * (l + 1) // 2 % 9) == 0 or r == 1 or r == 4 or r == 7:
m = tuple(10 ** (l - i - 1) for i in range(l))
for p in permutations(range(1, l + 1)):
if integer_nthroot(n := sum(prod(k) for k in zip(m, p)), 2)[1]:
yield n
def A352346_gen(): # generator of terms
n1, m1, n2, m2 = 1, 1, 2, 2
while True:
if m1 == m2:
yield m1
k = 0
while k == 0:
n1 += 2
m1 += (k := prod(int(d) for d in str(n1)))
while m2 < m1:
n2 += 2
m2 += prod(int(d) for d in str(n2))
def A352601(n):
return rf(2 * n, n)
def A124320_T(n, k):
return rf(n, k)
def A351826(n):
for k in count(1, 2):
c = 0
for j in count(1):
if k - 2**j < 2:
break
if isprime(k - 2**j) and isprime(k + 2**j):
c += 1
if c > n:
break
if c == n:
return k
def A352420(n):
return len(
set().union(
*(
primefactors((p ** ((e + 1) * n) - 1) // (p**n - 1))
for p, e in factorint(n).items()
)
)
)
def A352535_gen(startvalue=0): # generator of terms
return filter(
lambda m: not sum(
int(d) ** 2 * (-1 if i % 2 else 1) for i, d in enumerate(str(m))
),
count(max(startvalue, 0)),
)
def A351319(n):
return n if n <= 2 else int((k := isqrt(n)) ** 2 + k - n + 1 > 0)
def A352155_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10 ** max(m2, m5), 10 ** (t := n_order(10, n // 2**m2 // 5**m5)) - 1
c = k // n
s = str(m * k // n - c * m).zfill(t)
if s == "0" and min(str(c)) == "1":
yield n
elif "0" not in s and min(str(c).lstrip("0") + s) == "1":
yield n
def A352156_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10 ** max(m2, m5), 10 ** (t := n_order(10, n // 2**m2 // 5**m5)) - 1
c = k // n
s = str(m * k // n - c * m).zfill(t)
if s == "0" and min(str(c)) == "2":
yield n
elif "0" not in s and min(str(c).lstrip("0") + s) == "2":
yield n
def A352157_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10 ** max(m2, m5), 10 ** (t := n_order(10, n // 2**m2 // 5**m5)) - 1
c = k // n
s = str(m * k // n - c * m).zfill(t)
if "0" not in s and min(str(c).lstrip("0") + s) == "3":
yield n
def A352158_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10 ** max(m2, m5), 10 ** (t := n_order(10, n // 2**m2 // 5**m5)) - 1
c = k // n
s = str(m * k // n - c * m).zfill(t)
if s == "0" and min(str(c)) == "4":
yield n
elif "0" not in s and min(str(c).lstrip("0") + s) == "4":
yield n
def A352159_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10 ** max(m2, m5), 10 ** (t := n_order(10, n // 2**m2 // 5**m5)) - 1
c = k // n
s = str(m * k // n - c * m).zfill(t)
if s == "0" and min(str(c)) == "5":
yield n
elif "0" not in s and min(str(c).lstrip("0") + s) == "5":
yield n
def A352160_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10 ** max(m2, m5), 10 ** (t := n_order(10, n // 2**m2 // 5**m5)) - 1
c = k // n
s = str(m * k // n - c * m).zfill(t)
if "0" not in s and min(str(c).lstrip("0") + s) == "6":
yield n
if sys.version_info < (3, 10):
def A352631(n):
return (
-1
if n == 2
else min(
bin(k**2)[2:].count("0")
for k in range(1 + isqrt(2 ** (n - 1) - 1), 1 + isqrt(2**n))
)
)
else:
def A352631(n):
return (
-1
if n == 2
else min(
n - (k**2).bit_count()
for k in range(1 + isqrt(2 ** (n - 1) - 1), 1 + isqrt(2**n))
)
)
def A352375_gen(): # generator of terms
a = 5
while True:
yield (s := sum(int(d) for d in str(a)))
a += s
def A016096_gen(): # generator of terms
a = 9
while True:
yield a
a += sum(int(d) for d in str(a))
def A350813(n):
m = prod(islice(filter(lambda p: p % 4 == 1, sieve), n))
a = isqrt(m)
d = max(filter(lambda d: d <= a, divisors(m, generator=True)))
return (m // d - d) // 2
def A349708(n):
m = primorial(n + 1) // 2
a = isqrt(m)
d = max(filter(lambda d: d <= a, divisors(m, generator=True)))
return (m // d - d) // 2
@lru_cache(maxsize=None)
def A000793(n):
return 1 if n == 0 else max(lcm(i, A000793(n - i)) for i in range(1, n + 1))
def A352715_gen(): # generator of terms
yield 1
l1, s, b, bli = 1, 2, set(), 0
while True:
i = s
while True:
if not (i in b or bin(i & l1).count("1") != bli):
yield i
l1 = i
bli = l1.bit_length() // 2
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A352716_gen(): # generator of terms
yield 1
l1, s, b = 1, 2, set()
while True:
i = s
while True:
if not (i in b or bin(i & l1).count("1") % 2):
yield i
l1 = i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A000037(n):
return n + isqrt(n + isqrt(n))
def A000037_gen(startvalue=1): # generator of terms
k = isqrt(max(startvalue, 1))
for m in count(k):
yield from range(m**2 + 1, (m + 1) ** 2)
def A000217(n):
return n * (n + 1) // 2
def A000196(n):
return isqrt(n)
def A086849(n):
return (m := n + isqrt(n + isqrt(n))) * (m + 1) // 2 - (k := isqrt(m)) * (k + 1) * (
2 * k + 1
) // 6
def A086849_gen(): # generator of terms
c, k = 0, 1
while True:
for n in range(k**2 + 1, (k + 1) ** 2):
c += n
yield c
k += 1
def A352738_gen(): # generator of terms
c, k, ks, m, ms = 0, 1, 2, 1, 1
while True:
for n in range(ks, ks + 2 * k):
c += n
if c == ms:
yield c
elif c > ms:
ms += 2 * m + 1
m += 1
ks += 2 * k + 1
k += 1
def A308485(n):
return sum(
p * e
for m in range(prime(n) + 1, prime(n + 1))
for p, e in factorint(m).items()
)
def A351855_gen(): # generator of terms
c, k, ks, m, p, q = 0, 1, 2, 1, 4, 5
while True:
for n in range(ks, ks + 2 * k):
c += n
if c == m:
yield c
else:
while c > m:
m += p
p += 1
if p == q:
q = nextprime(q)
p += 1
ks += 2 * k + 1
k += 1
def A352813(n):
m = factorial(2 * n)
return (
0
if n == 0
else min(
abs((p := prod(d)) - m // p)
for d in combinations(range(2, 2 * n + 1), n - 1)
)
)
def A038667(n):
m = factorial(n)
return (
0
if n == 0
else min(
abs((p := prod(d)) - m // p)
for l in range(n, n // 2, -1)
for d in combinations(range(1, n + 1), l)
)
)
def A061057(n):
k = factorial(n)
m = max(d for d in divisors(k, generator=True) if d <= isqrt(k))
return k // m - m
def A263292(n):
m = factorial(n)
return (
1
if n == 0
else len(
set(
abs((p := prod(d)) - m // p)
for l in range(n, n // 2, -1)
for d in combinations(range(1, n + 1), l)
)
)
)
def A200744(n):
m = factorial(n)
return min(
(abs((p := prod(d)) - m // p), max(p, m // p))
for l in range(n, n // 2, -1)
for d in combinations(range(1, n + 1), l)
)[1]
def A200743(n):
m = factorial(n)
return min(
(abs((p := prod(d)) - m // p), min(p, m // p))
for l in range(n, n // 2, -1)
for d in combinations(range(1, n + 1), l)
)[1]
def A351744(n):
return int(str(n).translate({48: 49, 50: 51, 52: 53, 54: 55, 56: 57}))
def A106747(n):
return int(
str(n).translate(
{49: 48, 50: 49, 51: 49, 52: 50, 53: 50, 54: 51, 55: 51, 56: 52, 57: 52}
)
)
def A107130(n):
return int(str(n).translate({49: 48, 51: 49, 53: 50, 55: 51, 57: 52}))
def A306436(n):
return int(
str(n).translate(
{
48: 49,
49: 48,
50: 51,
51: 50,
52: 53,
53: 52,
54: 55,
55: 54,
56: 57,
57: 56,
}
)
)
def A107128(n):
return int(str(n).translate({50: 49, 52: 50, 54: 51, 56: 52}))
def A352788_gen(): # generator of terms
c, m, ms = 0, 1, 1
for n in count(1):
c += 1 if n <= 2 else n * totient(n) // 2
if c == ms:
yield c
else:
while c > ms:
ms += 2 * m + 1
m += 1
def A352148_gen(): # generator of terms
yield 0
for l in count(0):
for d in range(1, 10):
for m in range(2**l, 2 ** (l + 1)):
a, b = integer_nthroot(8 * d * int(bin(m)[2:]) + 1, 2)
if b:
yield (a - 1) // 2
def A353243_gen(): # generator of terms
k, c = Fraction(), 0
for n in count(1):
k += Fraction(1, n)
if c < (m := max(continued_fraction(k))):
c = m
yield n
def A353244_gen(): # generator of terms
k, c = Fraction(), 0
for n in count(1):
k += Fraction(1, n)
if c < (m := max(continued_fraction(k))):
yield (c := m)
def A023896(n):
return 1 if n == 1 else n * totient(n) // 2
def A103181(n):
return int("".join(str(int(d) % 2) for d in str(n)))
def A352881(n):
from sympy.abc import y, z
zc = Counter()
for x in range(1, 10**n + 1):
for d in diophantine(z * (x + y) - x * y):
if x <= d[0] <= 10 ** n and d[1] >= 0:
zc[d[1]] += 1
return sorted(zc.items(), key=lambda x: (-x[1], x[0]))[0][0]
def A352635(n):
cset, iset = set(), set()
for i in range(n):
if i not in iset:
j, jset, jlist = i, set(), []
while j not in jset:
jset.add(j)
jlist.append(j)
iset.add(j)
j = (j**2 + 1) % n
cset.add(min(jlist[jlist.index(j) :]))
return len(cset)
@lru_cache(maxsize=None)
def A352969_set(n):
if n == 0:
return {1}
return set(
sum(x) for x in combinations_with_replacement(A352969_set(n - 1), 2)
) | set(prod(x) for x in combinations_with_replacement(A352969_set(n - 1), 2))
def A353969(n):
return len(A352969_set(n))
def A263995(n):
return len(
set(sum(x) for x in combinations_with_replacement(range(1, n + 1), 2))
| set(prod(x) for x in combinations_with_replacement(range(1, n + 1), 2))
)
def A352040(n):
k = 10 * n - 1 + int(ceiling((10 * n - 1) * log(5, 2)))
s = str(c := 2**k)
while any(s.count(d) < n for d in "0123456789"):
c *= 2
k += 1
s = str(c)
return k
@lru_cache(maxsize=None)
def A352289(n):
return 1 if n == 1 else 2 * prime(A352289(n - 1))
def A064989(n):
return prod(1 if p == 2 else prevprime(p) * e for p, e in factorint(n).items())
def A252463(n):
return A064989(n) if n % 2 else n // 2
def A353412(n):
return int(
bin(
prod(1 if p == 2 else prevprime(p) * e for p, e in factorint(n).items())
if n % 2
else n // 2
)[2:].rstrip("0"),
2,
)
def A051064(n):
c = 1
a, b = divmod(n, 3)
while b == 0:
a, b = divmod(a, 3)
c += 1
return c
def A352992(n):
n10, n7 = 10**n, (10**n - 1) * 7 // 9
for m in count(1):
a, b = divmod(m**3, n10)
if b == n7 and a % 10 != 7:
return m
def A351374_gen(): # generator of terms
for k in range(1, 157):
a = tuple(i**k for i in range(20))
yield from (
x[0]
for x in sorted(
filter(
lambda x: x[0] > 0
and tuple(sorted(sympydigits(x[0], 20)[1:])) == x[1],
(
(sum(map(lambda y: a[y], b)), b)
for b in combinations_with_replacement(range(20), k)
),
)
)
)
def A010354_gen(): # generator of terms
for k in range(1, 30):
a = tuple(i**k for i in range(8))
yield from (
x[0]
for x in sorted(
filter(
lambda x: x[0] > 0
and tuple(int(d, 8) for d in sorted(oct(x[0])[2:])) == x[1],
(
(sum(map(lambda y: a[y], b)), b)
for b in combinations_with_replacement(range(8), k)
),
)
)
)
def A161953_gen(): # generator of terms
for k in range(1, 74):
a = tuple(i**k for i in range(16))
yield from (
x[0]
for x in sorted(
filter(
lambda x: x[0] > 0
and tuple(int(d, 16) for d in sorted(hex(x[0])[2:])) == x[1],
(
(sum(map(lambda y: a[y], b)), b)
for b in combinations_with_replacement(range(16), k)
),
)
)
)
def A352065(n):
plist = [prime(k) for k in range(1, 2 * n + 2)]
pd = prod(plist)
while True:
mlist = [nextprime(pd // (2 * n + 1) - 1)]
for _ in range(n):
mlist = [prevprime(mlist[0])] + mlist + [nextprime(mlist[-1])]
if sum(mlist) <= pd:
while (s := sum(mlist)) <= pd:
if s == pd:
return plist[0]
mlist = mlist[1:] + [nextprime(mlist[-1])]
else:
while (s := sum(mlist)) >= pd:
if s == pd:
return plist[0]
mlist = [prevprime(mlist[0])] + mlist[:-1]
pd //= plist[0]
plist = plist[1:] + [nextprime(plist[-1])]
pd *= plist[-1]
def A353073_gen(startvalue=3): # generator of terms
q = nextprime(max(startvalue, 3) - 1)
p, r = prevprime(q), nextprime(q)
while True:
if integer_nthroot(q - p, 2)[1] and integer_nthroot(r - q, 2)[1]:
yield q
t = q
for i in count(1):
t += 2 * i - 1
if t >= r:
break
if integer_nthroot(r - t, 2)[1]:
yield t
p, q, r = q, r, nextprime(r)
def A007918(n):
return nextprime(n - 1)
def A353088_gen(): # generator of terms
p, q, g, h = 3, 5, True, False
while True:
if g and h:
yield p
p, q = q, nextprime(q)
g, h = h, integer_nthroot(q - p, 2)[1]
def A353087(n):
k, m, r = 1, 1, 10 ** (10 * n - 1)
while m < r:
k += 1
m *= k
s = str(m)
while any(s.count(d) < n for d in "0123456789"):
k += 1
m *= k
s = str(m)
return k
def A353054_gen(): # generator of terms
for l in count(1):
a, b = 10**l - 2, 10 ** (l - 1) - 2
for m in range(1, 10):
q, r = divmod(m * a - 1, 19)
if r == 0 and b <= q - 2 <= a:
yield 10 * q + m
def A034180_gen(): # generator of terms
for l in count(1):
clist = []
for k in range(1, 10):
a, b = 10**l - k, 10 ** (l - 1) - k
for m in range(1, 10):
q, r = divmod(m * a - 1, 10 * k - 1)
if r == 0 and b <= q - k <= a:
clist.append(10 * q + m)
yield from sorted(clist)
def A035126_gen(): # generator of terms
for l in count(0):
l1, l2 = 10 ** (l + 1), 10**l
yield from sorted(
set(
x**2
for z in (diop_DN(10, m * (1 - l1)) for m in range(10))
for x, y in z
if l1 >= x**2 >= l2
)
)
def A035127_gen(): # generator of terms
for l in count(0):
l1, l2 = 10 ** (l + 1), 10**l
yield from sorted(
set(
y**2
for z in (diop_DN(10, m * (1 - l1)) for m in range(10))
for x, y in z
if l1 >= x**2 >= l2
)
)
def A045877_gen(): # generator of terms
for l in count(0):
l1, l2 = 10 ** (l + 1), 10**l
yield from sorted(
set(
abs(x)
for z in (diop_DN(10, m * (1 - l1)) for m in range(10))
for x, y in z
if l1 >= x**2 >= l2
)
)
def A045878_gen(): # generator of terms
for l in count(0):
l1, l2 = 10 ** (l + 1), 10**l
yield from sorted(
set(
abs(y)
for z in (diop_DN(10, m * (1 - l1)) for m in range(10))
for x, y in z
if l1 >= x**2 >= l2
)
)
def A353220(n):
return reduce(lambda x, _: (3 * x + 1) // 2, range(n), n)
def A353215(n):
return reduce(lambda x, _: (3 * x - 1) // 2, range(n), n)
def A353613_gen(startvalue=1): # generator of terms
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if set(
str(10 ** (max(m2, m5) + n_order(10, m // 2**m2 // 5**m5)) // m)
) <= {"0", "2", "4", "6", "8"}:
yield m
def A353614_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10 ** max(m2, m5), 10 ** (t := n_order(10, n // 2**m2 // 5**m5)) - 1
c = k // n
s = str(m * k // n - c * m).zfill(t)
if set(str(c).lstrip("0") + ("" if int(s) == 0 else s)) <= {
"1",
"3",
"5",
"7",
"9",
}:
yield n
def A338754(n):
return int("".join(d * 2 for d in str(n)))
def A338086(n):
return int("".join(d * 2 for d in gmpy2digits(n, 3)), 3)
def A351501(n):
return comb(m := n**2 + n - 1, n) // m
def A099306(n):
return A003415(A003415(A003415(n)))
def A068346(n):
return A003415(A003415(n))
def A353691_helper(n):
f = factorint(n).items()
return prod(p**e * (p - 1) * (e + 1) for p, e in f), prod(
p ** (e + 1) - 1 for p, e in f
)
def A353691(n):
Hnp, Hnq = A353691_helper(n)
g = gcd(Hnp, Hnq)
Hnp //= g
Hnq //= g
k = n + 1
Hkp, Hkq = A353691_helper(k)
while (Hkp * Hnq) % (Hkq * Hnp):
k += 1
Hkp, Hkq = A353691_helper(k)
return k
def A352940(n):
return (isqrt(n**2 * (n * (2 * n - 4) + 2) + 1) - 1) // 2
def A353709_gen(): # generator of terms
s, a, b, c, ab = {0, 1}, 0, 1, 2, 1
yield from (0, 1)
while True:
for n in count(c):
if not (n & ab or n in s):
yield n
a, b = b, n
ab = a | b
s.add(n)
while c in s:
c += 1
break
def A000005(n):
return divisor_count(n)
def A000010(n):
return totient(n)
def A000027(n):
return n
def A005117_gen(startvalue=1):
return filter(
lambda n: all(x == 1 for x in factorint(n).values()), count(max(startvalue, 1))
)
if sys.version_info >= (3, 10):
def A000069_gen(startvalue=0):
return filter(lambda n: n.bit_count() % 2, count(max(startvalue, 0)))
def A001969_gen(startvalue=0):
return filter(lambda n: not n.bit_count() % 2, count(max(startvalue, 0)))
else:
def A000069_gen(startvalue=0):
return filter(lambda n: bin(n).count("1") % 2, count(max(startvalue, 0)))
def A001969_gen(startvalue=0):
return filter(lambda n: not bin(n).count("1") % 2, count(max(startvalue, 0)))
def A002654(n):
return prod(
1 if p == 2 else (e + 1 if p % 4 == 1 else (e + 1) % 2)
for p, e in factorint(n).items()
)
def A353710_gen(): # generator of terms
s, a, b, c, ab = {0, 1}, 0, 1, 2, 1
yield from (0, 1)
while True:
for n in count(c):
if not (n & ab or n in s):
yield c
a, b = b, n
ab = a | b
s.add(n)
while c in s:
c += 1
break
def A353718_gen(): # generator of terms
s, a, b, c, ab, k = {0, 1}, 0, 1, 2, 1, 1
yield from (1, 1)
while True:
for n in count(c):
if not (n & ab or n in s):
a, b = b, n
ab = a | b
s.add(n)
if c in s:
yield k
k = 0
while c in s:
c += 1
k += 1
break
def A048785(n):
return 0 if n == 0 else prod(3 * e + 1 for e in factorint(n).values())
def A353551(n):
return sum(prod(3 * e + 1 for e in factorint(k).values()) for k in range(1, n + 1))
def A061503(n):
return sum(prod(2 * e + 1 for e in factorint(k).values()) for k in range(1, n + 1))
def A353789(n):
return prod(
(q := nextprime(p)) ** (e - 1) * p**e * (q - 1)
for p, e in factorint(n).items()
)
def A003961(n):
return prod(nextprime(p) ** e for p, e in factorint(n).items())
def A353906(n):
return sum(
(-1 if i % 2 else 1) * int(j) for i, j in enumerate(str(n)[::-1])
) ** len(str(n))
def A055017(n):
return sum((-1 if i % 2 else 1) * int(j) for i, j in enumerate(str(n)[::-1]))
def A002997_gen(): # generator of terms
p, q = 3, 5
while True:
for n in range(p + 2, q, 2):
f = factorint(n)
if max(f.values()) == 1 and not any((n - 1) % (p - 1) for p in f):
yield n
p, q = q, nextprime(q)
def A352970_gen(): # generator of terms
p, q = 3, 5
while True:
for n in range(p + 11 - ((p + 2) % 10), q, 10):
f = factorint(n)
if max(f.values()) == 1 and not any((n - 1) % (p - 1) for p in f):
yield n
p, q = q, nextprime(q)
def A011782(n):
return 1 if n == 0 else 2 ** (n - 1)
def A353715_gen(): # generator of terms
s, a, b, c, ab = {0, 1}, 0, 1, 2, 1
yield 1
while True:
for n in count(c):
if not (n & ab or n in s):
yield b + n
a, b = b, n
ab = a | b
s.add(n)
while c in s:
c += 1
break
def A353724_gen(): # generator of terms
s, a, b, c, ab = {0, 1}, 0, 1, 2, 1
yield 0
while True:
for n in count(c):
if not (n & ab or n in s):
yield len(t := bin(b + n)) - len(t.rstrip("0"))
a, b = b, n
ab = a | b
s.add(n)
while c in s:
c += 1
break
def A070939(n):
return 1 if n == 0 else n.bit_length()
if sys.version_info >= (3, 10):
def A353986_gen(): # generator of terms
a, b, k, ah = 1, 1, 1, 1
while True:
if ah == (bh := b.bit_count()):
yield k
a, b, ah = b, a + b, bh
k += 1
def A353987_gen(): # generator of terms
b, c, k, ah, bh = 1, 2, 1, 1, 1
while True:
if ah == (ch := c.bit_count()) == bh:
yield k
b, c, ah, bh = c, b + c, bh, ch
k += 1
else:
def A353986_gen(): # generator of terms
a, b, k, ah = 1, 1, 1, 1
while True:
if ah == (bh := bin(b).count("1")):
yield k
a, b, ah = b, a + b, bh
k += 1
def A353987_gen(): # generator of terms
b, c, k, ah, bh = 1, 2, 1, 1, 1
while True:
if ah == (ch := bin(c).count("1")) == bh:
yield k
b, c, ah, bh = c, b + c, bh, ch
k += 1
def A353728_gen(): # generator of terms
yield 1
l1, s, b = 1, 2, set()
while True:
i = s
while True:
if i & l1 and not i in b:
yield int(bin(i)[2:])
l1 = i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
if sys.version_info >= (3, 10):
def A352202_gen(): # generator of terms
yield 1
l1, s, b = 1, 2, set()
while True:
i = s
while True:
if i & l1 and not i in b:
yield i.bit_count()
l1 = i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
else:
def A352202_gen(): # generator of terms
yield 1
l1, s, b = 1, 2, set()
while True:
i = s
while True:
if i & l1 and not i in b:
yield bin(i).count("1")
l1 = i
b.add(i)
while s in b:
b.remove(s)
s += 1
break
i += 1
def A352979(n):
return (
n**2
* (
n
* (
n
* (
n
* (
n
* (
n
* (
n
* (n * (n * (n * (35 * n + 450) + 2293) + 5700) + 6405)
+ 770
)
- 3661
)
- 240
)
+ 2320
)
+ 40
)
- 672
)
// 13440
)
def A353021(n):
return (
n
* (
n
* (
n
* (
n
* (
n
* (
n
* (
n
* (
n
* (
8
* n
* (n * (70 * n * (5 * n + 84) + 40417) + 144720)
+ 2238855
)
+ 2050020
)
+ 207158
)
- 810600
)
- 58505
)
+ 322740
)
+ 7956
)
- 45360
)
// 5443200
)
def A353618_gen(): # generator of terms
for b in count(1):
q, c = 2, 8
while c < b:
d = (b - c) ** 2 * (b + c)
s, t = divmod(d, c)
if t == 0:
a, r = integer_nthroot(s, 2)
if r and b - c < a < b + c and gcd(a, b, q) == 1:
yield from (a, b, c)
c += q * (3 * q + 3) + 1
q += 1
def A353729_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = str(n)
if not (
"0" in s
or any(int("0" + s[:i] + s[i + 1 :]) % int(s[i]) for i in range(len(s)))
):
yield n
def A268631(n):
return (
1
- 2 * n
+ prod(p ** (e - 1) * ((p - 1) * e + p) for p, e in factorint(n).items())
)
def A006579(n):
return prod(p ** (e - 1) * ((p - 1) * e + p) for p, e in factorint(n).items()) - n
def A352980(n):
return (
n**2
* (
n
* (
n
* (
n
* (
n
* (
n
* (
n * (n * (n * (n * (35 * n - 30) - 347) + 180) + 1365)
- 350
)
- 2541
)
+ 240
)
+ 2160
)
- 40
)
- 672
)
// 13440
)
def A045584_gen(startvalue=1): # generator of terms
kstart = max(startvalue, 1)
k3, k4 = 3**kstart, 4**kstart
for k in count(kstart):
if (k3 + k4) % k == 0:
yield k
k3 *= 3
k4 *= 4
def A088534(n):
c = 0
for y in range(n + 1):
if y**2 > n:
break
for x in range(y + 1):
z = x * (x + y) + y**2
if z > n:
break
elif z == n:
c += 1
return c
def A198775_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
c = 0
for y in range(n + 1):
if c > 4 or y**2 > n:
break
for x in range(y + 1):
z = x * (x + y) + y**2
if z > n:
break
elif z == n:
c += 1
if c > 4:
break
if c == 4:
yield n
def A335951_T(n, k):
z = (
simplify(
(bernoulli(2 * n, (sqrt(8 * symbolx + 1) + 1) / 2) - bernoulli(2 * n, 1))
/ (2 * n)
)
.as_poly()
.all_coeffs()
)
return z[n - k] * lcm(*(d.q for d in z))
def A335951_gen(): # generator of terms
yield from (A335951_T(n, k) for n in count(0) for k in range(n + 1))
def A335952(n):
return lcm(
*(
d.q
for d in simplify(
(
bernoulli(2 * n, (sqrt(8 * symbolx + 1) + 1) / 2)
- bernoulli(2 * n, 1)
)
/ (2 * n)
)
.as_poly()
.all_coeffs()
)
)
if sys.version_info >= (3, 10):
def A354112(n):
return sum(d.bit_count() for d in divisors(2**n - 1, generator=True))
else:
def A354112(n):
return sum(bin(d).count("1") for d in divisors(2**n - 1, generator=True))
def A353943(n):
return (
2**10 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**10, True)[1])
)
def A353942(n):
return (
2**9 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**9, True)[1])
)
def A353941(n):
return (
2**8 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**8, True)[1])
)
def A353940(n):
return (
2**7 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**7, True)[1])
)
def A353939(n):
return (
2**6 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**6, True)[1])
)
def A353938(n):
return (
2**5 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**5, True)[1])
)
def A353937(n):
return (
2**4 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**4, True)[1])
)
def A249275(n):
return (
2**3 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**3, True)[1])
)
def A034939(n):
return int(sqrt_mod(-1, 5**n))
def A257833_T(n, k):
return (
2**k + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**k, True)[1])
)
def A257833_gen(): # generator of terms
yield from (A257833_T(n, i - n + 2) for i in count(1) for n in range(i, 0, -1))
def A352395(n):
return sum(
Fraction(-1 if k % 2 else 1, 2 * k + 1) for k in range(n + 1)
).denominator
def A263445(n):
return (2 * n + 1) * factorial(n + 1) * bernoulli(2 * n)
def A039678(n):
return (
2**2 + 1
if n == 1
else int(nthroot_mod(1, (p := prime(n)) - 1, p**2, True)[1])
)
def A185103(n):
z = nthroot_mod(1, n - 1, n**2, True)
return int(z[0] + n**2 if len(z) == 1 else z[1])
def A256517(n):
z = nthroot_mod(1, (c := composite(n)) - 1, c**2, True)
return int(z[0] + c**2 if len(z) == 1 else z[1])
def A255885(n):
for b in count(1):
if n == sum(
1 for c in range(2, b + 1) if not isprime(c) and pow(b, c - 1, c**2) == 1
):
return b
def A255885_gen(): # generator of terms
A255885_dict, n = {}, 1
for b in count(1):
d = sum(
1 for c in range(2, b + 1) if not isprime(c) and pow(b, c - 1, c**2) == 1
)
if d not in A255885_dict:
A255885_dict[d] = b
if n in A255885_dict:
yield A255885_dict[n]
n += 1
def A255901(n):
for b in count(1):
if n == sum(1 for p in primerange(2, b + 1) if pow(b, p - 1, p**2) == 1):
return b
def A255901_gen(): # generator of terms
A255901_dict, n = {}, 1
for b in count(1):
c = sum(1 for p in primerange(2, b + 1) if pow(b, p - 1, p**2) == 1)
if c not in A255901_dict:
A255901_dict[c] = b
if n in A255901_dict:
yield A255901_dict[n]
n += 1
def A287147_gen(): # generator of terms
c, p = 5, 3
yield 2
while True:
d = nthroot_mod(1, p - 1, p**2, True)[1]
if d > c:
c = d
yield p
p = nextprime(p)
def A353730_gen(): # generator of terms
aset, aqueue, c, f = {2}, deque([2]), 1, True
yield 2
while True:
for m in count(c):
if m not in aset and all(gcd(m, a) == 1 for a in aqueue):
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
f = not f
while c in aset:
c += 1
break
def A247665_gen(): # generator of terms
aset, aqueue, c, f = {2}, deque([2]), 3, True
yield 2
while True:
for m in count(c):
if m not in aset and all(gcd(m, a) == 1 for a in aqueue):
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
f = not f
while c in aset:
c += 1
break
def A249559_gen(): # generator of terms
aset, aqueue, c, f = {3}, deque([3]), 2, True
yield 3
while True:
for m in count(c):
if m not in aset and all(gcd(m, a) == 1 for a in aqueue):
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
f = not f
while c in aset:
c += 1
break
def A352808_gen(): # generator of terms
aset, aqueue, c, m, f = {0}, deque(), 1, 0, False
yield 0
for n in count(1):
if f:
m = aqueue.popleft()
f = not f
for a in count(c):
if not (a & m or a in aset):
yield a
aset.add(a)
aqueue.append(a)
while c in aset:
c += 1
break
def A354210(n):
return int(isqrt(prod(fib2(n + 1))))
def A001654(n):
return prod(fib2(n + 1))
def A353051(n):
while n > 1 and len(f := factorint(n, multiple=True)) > 1:
n -= sum(f)
return n
def A075255(n):
return n - sum(factorint(n, multiple=True))
def A351396_gen(startvalue=1): # generator of terms
return filter(
lambda d: not (
isprime(d)
or (
p := n_order(
10, d // 2 ** multiplicity(2, d) // 5 ** multiplicity(5, d)
)
)
<= 1
or (d - 1) % p
),
count(max(startvalue, 1)),
)
def A350220_gen(): # generator of terms
pset = set()
for d in count(1):
if not (
isprime(d)
or (
p := n_order(
10, d // 2 ** multiplicity(2, d) // 5 ** multiplicity(5, d)
)
)
<= 1
or (d - 1) % p
or p in pset
):
yield d
pset.add(p)
def A350598_gen(): # generator of terms
pset = set()
for d in count(1):
if not isprime(d):
m2, m5 = multiplicity(2, d), multiplicity(5, d)
r = max(m2, m5)
k, m = 10**r, 10 ** (t := n_order(10, d // 2**m2 // 5**m5)) - 1
c = k // d
s = str(m * k // d - c * m).zfill(t)
if not (t <= 1 or (d - 1) % t or s in pset):
yield d
pset.add(s)
def A353507(n):
return (
0 if n == 1 else prod(len(list(g)) for k, g in groupby(factorint(n).values()))
)
def A353503_gen(startvalue=1): # generator of terms
return filter(
lambda n: n == 1
or prod((f := factorint(n)).values())
== prod(primepi(p) ** e for p, e in f.items()),
count(max(startvalue, 1)),
)
def A353397(n):
return prod(prime(2 ** primepi(p)) ** e for p, e in factorint(n).items())
def A090252_gen(): # generator of terms
aset, aqueue, c, b, f = {1}, deque([1]), 2, 1, True
yield 1
while True:
for m in count(c):
if m not in aset and gcd(m, b) == 1:
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = lcm(*aqueue)
f = not f
while c in aset:
c += 1
break
def A354255_gen(): # generator of terms
aset, aqueue, c, plist, f = {1}, deque([1]), 2, [], True
yield 1
while True:
for m in count(c):
if m not in aset and all(m % p for p in plist):
if not m % 2:
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
plist = list(set().union(*(primefactors(a) for a in aqueue)))
f = not f
while c in aset:
c += 1
break
def A319571_gen(): # generator of terms
for n in count(0):
for m in range(n + 1):
yield from (m, n - m) if n % 2 else (n - m, m)
def A353029(n):
return 2**n * n * (n * (n * (n * (n * (n - 6) + 11) - 4) - 6) + 4) // 6
def A351632(n):
return 2**n * n * (n * (n * (n * (n - 7) + 17) - 17) + 6) // 6
def A234848_gen():
return chain(
(0,),
(
n
for n in (
int("".join(i))
for l in count(1)
for i in combinations_with_replacement("123456789", l)
)
if integer_nthroot(8 * n + 1, 2)[1]
),
)
def A004647(n):
return int(oct(2**n)[2:])
def A354256_gen(): # generator of terms
for l in count(2, 2):
for m in (1, 4, 5, 6, 9):
for k in range(
1 + isqrt(m * 10 ** (l - 1) - 1), 1 + isqrt((m + 1) * 10 ** (l - 1) - 1)
):
if k % 10 and integer_nthroot(int(str(k * k)[::-1]), 2)[1]:
yield k * k
def A353990_gen(): # generator of terms
yield 1
a, s, b = 1, 2, set()
while True:
for i in count(s):
if not (i == a + 1 or i & a or gcd(i, a) > 1 or i in b):
yield i
a = i
b.add(i)
while s in b:
s += 1
break
def A114112(n):
return n + (0 if n <= 2 else -1 + 2 * (n % 2))
def A114113(n):
return 1 if n == 1 else (m := n // 2) * (n + 1) + (n + 1 - m) * (n - 2 * m)
def A033999(n):
return -1 if n % 2 else 1
def A354008(n):
return (
1
if n == 1
else (k := (m := n // 2) * (n + 1) + (n + 1 - m) * (n - 2 * m)) // gcd(k, n)
)
def A141310(n):
return 2 if n % 2 else n + 1
def A130883(n):
return n * (2 * n - 1) + 1
def A128918(n):
return n * (n - 1) // 2 + 1 + (n - 1) * (n % 2)
def A131179(n):
return n * (n + 1) // 2 + (1 - n) * (n % 2)
def A008836(n):
return -1 if sum(factorint(n).values()) % 2 else 1
def A354334(n):
return sum(Fraction(1, factorial(2 * k)) for k in range(n + 1)).numerator
def A354335(n):
return sum(Fraction(1, factorial(2 * k)) for k in range(n + 1)).denominator
def A354332(n):
return sum(
Fraction(-1 if k % 2 else 1, factorial(2 * k + 1)) for k in range(n + 1)
).numerator
def A354333(n):
return sum(
Fraction(-1 if k % 2 else 1, factorial(2 * k + 1)) for k in range(n + 1)
).denominator
def A354211(n):
return sum(Fraction(1, factorial(2 * k + 1)) for k in range(n + 1)).numerator
def A354331(n):
return sum(Fraction(1, factorial(2 * k + 1)) for k in range(n + 1)).denominator
def A352962_gen(): # generator of terms
a = 2
yield a
for n in count(2):
yield (a := min(n, a) if gcd(n, a) == 1 else n + 2)
def A354354(n):
return int(not n % 6 & 3 ^ 1)
def A120325(n):
return int(not (n + 3) % 6 & 3 ^ 1)
def A232991(n):
return int(not (n + 1) % 6 & 3 ^ 1)
def A000035(n):
return n & 1
def A059841(n):
return 1 - (n & 1)
def A000034(n):
return 1 + (n & 1)
def A011655(n):
return int(bool(n % 3))
def A088911(n):
return int(n % 6 < 3)
def A010702(n):
return 3 + (n & 1)
def A010718(n):
return 5 + 2 * (n & 1)
def A010883(n):
return 1 + (n & 3)
def A132429(n):
return 3 - 2 * (n & 3)
def A010887(n):
return 1 + (n & 7)
def A354404(n):
return sum(
Fraction(1 if k & 1 else -1, k * factorial(k)) for k in range(1, n + 1)
).denominator
def A354402(n):
return sum(
Fraction(1 if k & 1 else -1, k * factorial(k)) for k in range(1, n + 1)
).numerator
def A353545(n):
return sum(Fraction(1, k * factorial(k)) for k in range(1, n + 1)).numerator
def A354401(n):
return sum(Fraction(1, k * factorial(k)) for k in range(1, n + 1)).denominator
def A353848_gen(startvalue=1): # generator of terms
return filter(
lambda n: n == 1
or (
sum((f := factorint(n)).values()) > 1
and len(set(primepi(p) * e for p, e in f.items())) <= 1
),
count(max(startvalue, 1)),
)
def A000179(n):
return (
1
if n == 0
else sum(
(-2 * n if k & 1 else 2 * n)
* comb(m := 2 * n - k, k)
* factorial(n - k)
// m
for k in range(n + 1)
)
)
def A354432(n):
f = factorint(n)
return (
Fraction(
prod(p ** (e + 1) - 1 for p, e in f.items()), prod(p - 1 for p in f) * n
)
- sum(Fraction(1, p) for p in f)
).numerator
def A354433(n):
f = factorint(n)
return (
Fraction(
prod(p ** (e + 1) - 1 for p, e in f.items()), prod(p - 1 for p in f) * n
)
- sum(Fraction(1, p) for p in f)
).denominator
def A354437(n):
return sum(factorial(n) * (-k) ** (n - k) // factorial(k) for k in range(n + 1))
def A354436(n):
return sum(factorial(n) * k ** (n - k) // factorial(k) for k in range(n + 1))
def A354154_gen(): # generator of terms
aset, aqueue, c, b, f, p = {1}, deque([1]), 2, 1, True, 2
yield 0
while True:
for m in count(c):
if m not in aset and gcd(m, b) == 1:
yield p - m
p = nextprime(p)
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = lcm(*aqueue)
f = not f
while c in aset:
c += 1
break
def A297330(n):
s = str(n)
return sum(abs(int(s[i]) - int(s[i + 1])) for i in range(len(s) - 1))
def A354212_gen(startvalue=1): # generator of terms
for n in count(max(startvalue, 1)):
s = str(n)
t = str(n * sum(abs(int(s[i]) - int(s[i + 1])) for i in range(len(s) - 1)))
if s != t and sorted(s) == sorted(t):
yield n
def A118478(n):
return (
1
if n == 1
else int(
min(
min(
crt((m, (k := primorial(n)) // m), (0, -1))[0],
crt((k // m, m), (0, -1))[0],
)
for m in (
prod(d)
for l in range(1, n // 2 + 1)
for d in combinations(sieve.primerange(prime(n) + 1), l)
)
)
)
)
def A215021(n):
return (
1
if n == 1
else (
s := int(
min(
min(
crt((m, (k := primorial(n)) // m), (0, -1))[0],
crt((k // m, m), (0, -1))[0],
)
for m in (
prod(d)
for l in range(1, n // 2 + 1)
for d in combinations(sieve.primerange(prime(n) + 1), l)
)
)
)
)
* (s + 1)
// k
)
def A214089(n):
return (
3
if n == 1
else int(
min(
filter(
isprime,
(
crt(tuple(sieve.primerange(prime(n) + 1)), t)[0]
for t in product((1, -1), repeat=n)
),
)
)
)
)
def A345988(n):
if n == 1:
return 2
plist = tuple(p**q for p, q in factorint(n).items())
return (
n * (n - 1)
if len(plist) == 1
else (
s := int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
* (s + 1)
)
def A215085(n):
return (
1
if n == 1
else (
int(
min(
filter(
isprime,
(
crt(tuple(sieve.primerange(prime(n) + 1)), t)[0]
for t in product((1, -1), repeat=n)
),
)
)
)
** 2
- 1
)
// 4
// primorial(n)
)
def A354160_gen(): # generator of terms
aset, aqueue, c, b, f = {1}, deque([1]), 2, 1, True
while True:
for m in count(c):
if m not in aset and gcd(m, b) == 1:
if len(fm := factorint(m)) == sum(fm.values()) == 2:
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = lcm(*aqueue)
f = not f
while c in aset:
c += 1
break
def A354161_gen(): # generator of terms
aset, aqueue, c, b, f, i = {1}, deque([1]), 2, 1, True, 1
while True:
for m in count(c):
if m not in aset and gcd(m, b) == 1:
i += 1
if len(fm := factorint(m)) == sum(fm.values()) == 2:
yield i
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = lcm(*aqueue)
f = not f
while c in aset:
c += 1
break
def A354162_gen(): # generator of terms
aset, aqueue, c, b, f = {1}, deque([1]), 2, 1, True
while True:
for m in count(c):
if m not in aset and gcd(m, b) == 1:
if m % 2 and len(fm := factorint(m)) == sum(fm.values()) == 2:
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = lcm(*aqueue)
f = not f
while c in aset:
c += 1
break
def A354163_gen(): # generator of terms
aset, aqueue, c, b, f, i = {1}, deque([1]), 2, 1, True, 1
while True:
for m in count(c):
if m not in aset and gcd(m, b) == 1:
i += 1
if m % 2 and len(fm := factorint(m)) == sum(fm.values()) == 2:
yield i
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = lcm(*aqueue)
f = not f
while c in aset:
c += 1
break
def A354443(n):
return fibonacci(pow(n, n, A001175(n))) % n
def A060305(n):
x, p = (1, 1), prime(n)
for k in count(1):
if x == (0, 1):
return k
x = (x[1], (x[0] + x[1]) % p)
def A345983_gen(): # generator of terms
c = 1
for n in count(2):
yield c
plist = tuple(p**q for p, q in factorint(n).items())
c += (
n - 1
if len(plist) == 1
else int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
def A345984_gen(): # generator of terms
c = 1
for n in count(4, 2):
yield c
plist = tuple(p**q for p, q in factorint(n).items())
c += (
n - 1
if len(plist) == 1
else int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
def A344875(n):
return prod(
(p ** (1 + e) if p == 2 else p**e) - 1 for p, e in factorint(n).items()
)
def A345992(n):
if n == 1:
return 1
plist = tuple(p**q for p, q in factorint(n).items())
return (
1
if len(plist) == 1
else gcd(
n,
int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
),
)
)
def A214149(n):
return (
7
if n == 1
else int(
min(
filter(
lambda n: n > 3 and isprime(n),
(
crt(tuple(sieve.primerange(5, prime(n + 2) + 1)), t)[0]
for t in product((3, -3), repeat=n)
),
)
)
)
)
def A214150(n):
return (
19
if n == 1
else int(
min(
filter(
lambda n: n > 5 and isprime(n),
(
crt(tuple(sieve.primerange(7, prime(n + 3) + 1)), t)[0]
for t in product((5, -5), repeat=n)
),
)
)
)
)
def A354463(n):
c, m = 0, 2**n
while m >= 5:
m //= 5
c += m
return c
def A070824(n):
return 0 if n == 1 else divisor_count(n) - 2
def A078709(n):
return n // divisor_count(n)
def A353960_gen(): # generator of terms
adict, a = {}, 1
yield a
while True:
if a in adict:
adict[a] += 1
a *= adict[a]
else:
adict[a] = 1
a //= divisor_count(a)
yield a
def A130290(n):
return prime(n) // 2
def A005097(n):
return prime(n + 1) // 2
def A354169_gen(): # generator of terms
aset, aqueue, b, f = {0, 1, 2}, deque([2]), 2, False
yield from (0, 1, 2)
while True:
for k in count(1):
m, j, j2, r, s = 0, 0, 1, b, k
while r > 0:
r, q = divmod(r, 2)
if not q:
s, y = divmod(s, 2)
m += y * j2
j += 1
j2 *= 2
if s > 0:
m += s * 2 ** b.bit_length()
if m not in aset:
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = reduce(or_, aqueue)
f = not f
break
def A354757_gen(): # generator of terms
aset, aqueue, b, f = {0, 1, 2}, deque([2]), 2, False
yield from (0, 0, 1)
while True:
for k in count(1):
m, j, j2, r, s = 0, 0, 1, b, k
while r > 0:
r, q = divmod(r, 2)
if not q:
s, y = divmod(s, 2)
m += y * j2
j += 1
j2 *= 2
if s > 0:
m += s * 2 ** b.bit_length()
if m not in aset:
yield sum(aqueue)
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = reduce(or_, aqueue)
f = not f
break
def A354680_gen(): # generator of terms
aset, aqueue, b, f = {0, 1, 2}, deque([2]), 2, False
yield 0
while True:
for k in count(1):
m, j, j2, r, s = 0, 0, 1, b, k
while r > 0:
r, q = divmod(r, 2)
if not q:
s, y = divmod(s, 2)
m += y * j2
j += 1
j2 *= 2
if s > 0:
m += s * 2 ** b.bit_length()
if m not in aset:
if bin(m).count("1") > 1:
yield m
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = reduce(or_, aqueue)
f = not f
break
def A354798_gen(): # generator of terms
aset, aqueue, b, f, i = {0, 1, 2}, deque([2]), 2, False, 2
yield 0
while True:
for k in count(1):
m, j, j2, r, s = 0, 0, 1, b, k
while r > 0:
r, q = divmod(r, 2)
if not q:
s, y = divmod(s, 2)
m += y * j2
j += 1
j2 *= 2
if s > 0:
m += s * 2 ** b.bit_length()
if m not in aset:
i += 1
if bin(m).count("1") > 1:
yield i
aset.add(m)
aqueue.append(m)
if f:
aqueue.popleft()
b = reduce(or_, aqueue)
f = not f
break
def A054055(n):
return max(int(d) for d in str(n))
def A095815(n):
return n + max(int(d) for d in str(n))
def A016116(n):
return 1 << n // 2
def A007590(n):
return n**2 // 2
def A000212(n):
return n**2 // 3
def A008615(n):
return n // 2 - n // 3
def A074148(n):
return n + n**2 // 2
def A098844_gen(): # generator of terms
aqueue, f, b = deque([]), False, 1
yield 1
for i in count(2):
yield (a := i * b)
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A098844(n):
return n * prod(n // 2**k for k in range(1, n.bit_length() - 1))
def A033485_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (1, 2)
while True:
a += b
yield a
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A040039_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (1, 1, 2, 2)
while True:
a += b
yield from (a, a)
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A178855_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
while True:
a += b
aqueue.append(a)
if f:
yield (a - 1) // 2
b = aqueue.popleft()
f = not f
def A094451_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (1, 2)
while True:
a = (a + b) % 3
yield a
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A008794(n):
return (n // 2) ** 2
@lru_cache(maxsize=None)
def A320225(n):
return 1 if n == 1 else sum(A320225(d) * (n // d - 1) for d in range(1, n))
def A320225_gen(): # generator of terms
alist, a = [1], 1
yield a
for n in count(2):
a = sum(alist[d - 1] * (n // d - 1) for d in range(1, n))
yield a
alist.append(a)
def A347027_gen(): # generator of terms
aqueue, f, b, a = deque([3]), True, 1, 3
yield from (1, 3)
while True:
a += 2 * b
yield a
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A346912_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (1, 3, 7)
while True:
a += b
yield 4 * a - 1
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A102378_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (1, 3)
while True:
a += b
yield 2 * a - 1
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A062187_gen(): # generator of terms
aqueue, f, b, a = deque([1]), True, 0, 1
yield from (0, 1)
while True:
a -= b
yield a
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A062186_gen(): # generator of terms
aqueue, f, b, a = deque([0]), True, 1, 0
yield from (1, 0)
while True:
a -= b
yield a
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A062188_gen(): # generator of terms
aqueue, f, b, a = deque([1]), True, 0, 1
yield from (0, 1)
while True:
a += b
yield a
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A022907_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (0, 2, 5)
while True:
a += b
yield 3 * a - 1
aqueue.append(a)
if f:
b = aqueue.popleft()
f = not f
def A022905_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield 1
while True:
a += b
aqueue.append(a)
if f:
yield (3 * a - 1) // 2
b = aqueue.popleft()
f = not f
def A022908_gen(): # generator of terms
aqueue, f, b, a = deque([2]), True, 1, 2
yield from (0, 2)
while True:
a += b
aqueue.append(a)
if f:
yield (3 * a + 1) // 2
b = aqueue.popleft()
f = not f
def A352717_gen(): # generator of terms
a, b = 1, 3
while True:
yield from (a,) * (b - a)
a, b = b, a + b
def A130241_gen(): # generator of terms
a, b = 1, 3
for i in count(1):
yield from (i,) * (b - a)
a, b = b, a + b
def A130247_gen(): # generator of terms
yield from (1, 0)
a, b = 3, 4
for i in count(2):
yield from (i,) * (b - a)
a, b = b, a + b
def A130242_gen(): # generator of terms
yield from (0, 0, 0, 2)
a, b = 3, 4
for i in count(3):
yield from (i,) * (b - a)
a, b = b, a + b
def A130245_gen(): # generator of terms
yield from (0, 1, 2)
a, b = 3, 4
for i in count(3):
yield from (i,) * (b - a)
a, b = b, a + b
def A130249_gen(): # generator of terms
a, b = 0, 1
for i in count(0):
yield from (i,) * (b - a)
a, b = b, 2 * a + b
def A130249(n):
return (3 * n + 1).bit_length() - 1
def A276710_gen(): # generator of terms
p, q = 3, 5
while True:
for m in range(p + 1, q):
r = m ** (m - 1)
c = 1
for k in range(m + 1):
c = c * comb(m, k) % r
if c == 0:
yield m
p, q = q, nextprime(q)
def A353010_gen(): # generator of terms
p, q = 3, 5
while True:
for m in range(p + 1, q):
r = m ** (m - 1)
c = 1
for k in range(m + 1):
c = c * comb(m, k) % r
if c == 0:
d, (e, f) = -m, divmod(prod(comb(m, k) for k in range(m + 1)), m)
while f == 0:
d += 1
e, f = divmod(e, m)
yield d
p, q = q, nextprime(q)
def A351628_gen(): # generator of terms
a, b, c = 1, 3, 0
while True:
yield from (c + i * a for i in range(1, b - a + 1))
a, b, c = b, a + b, c + a * (b - a)
def A001250_gen(): # generator of terms
yield from (1, 1)
blist = (0, 2)
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=0)))[-1]
def A348615_gen(): # generator of terms
yield from (0, 0)
blist, f = (0, 2), 1
for n in count(2):
f *= n
yield f - (blist := tuple(accumulate(reversed(blist), initial=0)))[-1]
def A354862(n):
f = factorial(n)
return sum(
f * (a := factorial(n // d)) // (b := factorial(d))
+ (f * b // a if d**2 < n else 0)
for d in divisors(n, generator=True)
if d**2 <= n
)
def A354863(n):
f = factorial(n)
return sum(f * n // d // factorial(d) for d in divisors(n, generator=True))
def A067742(n):
return sum(1 for d in divisors(n, generator=True) if n <= 2 * d**2 < 4 * n)
def A319529_gen(startvalue=1): # generator of terms
for k in count(max(1, startvalue + 1 - (startvalue & 1)), 2):
if any((k <= 2 * d**2 < 4 * k for d in divisors(k, generator=True))):
yield k
def A132049_gen(): # generator of terms
yield 2
blist = (0, 1)
for n in count(2):
yield Fraction(
2 * n * blist[-1],
(blist := tuple(accumulate(reversed(blist), initial=0)))[-1],
).numerator
def A132050_gen(): # generator of terms
yield 1
blist = (0, 1)
for n in count(2):
yield Fraction(
2 * n * blist[-1],
(blist := tuple(accumulate(reversed(blist), initial=0)))[-1],
).denominator
def A000708_gen(): # generator of terms
yield -1
blist = (0, 1)
for n in count(2):
yield -2 * blist[-1] + (blist := tuple(accumulate(reversed(blist), initial=0)))[
-1
]
def A024255_gen(): # generator of terms
yield from (0, 1)
blist = (0, 1)
for n in count(2):
yield n * (
blist := tuple(
accumulate(
reversed(tuple(accumulate(reversed(blist), initial=0))), initial=0
)
)
)[-1]
def A141479_gen(): # generator of terms
yield from (2, 3)
blist = (0, 1)
for n in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=0)))[-1] + (
2,
1,
1,
2,
)[n & 3]
def A000756_gen(): # generator of terms
yield from (1, 2)
blist = (1, 2)
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=0)))[-1]
def A180942_gen(): # generator of terms
blist = (0, 1)
for n in count(2):
blist = tuple(accumulate(reversed(blist), initial=0))
if (
n & 1
and (blist[-1] + (1 if (n - 1) // 2 & 1 else -1)) % n == 0
and not isprime(n)
):
yield n
def A166298_gen(): # generator of terms
yield 0
blist, c = (0, 1), 1
for n in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=0)))[-1] - c
c = c * (4 * n + 2) // (n + 2)
def A338399_gen(): # generator of terms
blist, a, b = tuple(), 0, 1
while True:
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=a))
)[-1]
a, b = b, a + b
def A338398_gen(): # generator of terms
blist = tuple()
for i in count(1):
yield (
blist := tuple(
accumulate(reversed(blist), func=operator_sub, initial=prime(i))
)
)[-1]
def A338400_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (
blist := tuple(
accumulate(reversed(blist), func=operator_sub, initial=npartitions(i))
)
)[-1]
def A102590_gen(): # generator of terms
blist, m = tuple(), 1
while True:
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=m))
)[-1]
m *= 2
def A062162_gen(): # generator of terms
blist, m = tuple(), -1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=(m := -m))))[-1]
def A097953_gen(): # generator of terms
blist, m = tuple(), 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=(m + 1) // 2)))[-1]
m *= -2
def A000667_gen(): # generator of terms
blist = tuple()
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=1)))[-1]
def A061531_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m = mobius(i)
def A306822_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m = m * (4 * i - 2) // i
def A307595_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (
blist := tuple(
accumulate(
reversed(blist), initial=hyperexpand(hyper((1 - i, -i), [], 1))
)
)
)[-1]
def A308521_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 2 * i
def A337445_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=m))
)[-1]
m *= i
def A308681_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=m))
)[-1]
m *= 2 * i - 1
def A337443_gen(): # generator of terms
blist = tuple()
for i in count(1):
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=i))
)[-1]
def A337444_gen(): # generator of terms
blist = tuple()
for i in count(1, 2):
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=i))
)[-1]
def A337446_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(0):
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=c))
)[-1]
c = c * (4 * i + 2) // (i + 2)
def A347071_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (
blist := tuple(accumulate(reversed(blist), func=operator_sub, initial=m))
)[-1]
m = m * i + 1
def A337447_gen(): # generator of terms
yield from (1, 0)
blist, alist = (1, 0), (1,)
while True:
yield (
blist := tuple(
accumulate(
reversed(blist),
func=operator_sub,
initial=(alist := list(accumulate(alist, initial=alist[-1])))[-1],
)
)
)[-1]
def A230960_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= i
def A000738_gen(): # generator of terms
blist, a, b = tuple(), 0, 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
a, b = b, a + b
def A000747_gen(): # generator of terms
blist = tuple()
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=prime(i))))[-1]
def A000753_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c = c * (4 * i + 2) // (i + 2)
def A231179_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
def A000718_gen(): # generator of terms
yield 1
blist, c = (1,), 1
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c += i
def A000674_gen(): # generator of terms
yield 1
blist = (1,)
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=2)))[-1]
def A101473_gen(): # generator of terms
blist, a, b = tuple(), 0, 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
a, b = b, 2 * a + b
def A101474_gen(): # generator of terms
blist, a, b = tuple(), 0, -1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
a, b = -b, -2 * a - b
def A307594_gen(): # generator of terms
blist, a, b = tuple(), 1, -1
for n in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
a, b = a * n + b, -b
def A306799_gen(): # generator of terms
blist, a = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
a = 2 * a * i // (i + 1) if i & 1 else 2 * a
def A307592_gen(): # generator of terms
blist = (1, 2)
yield from blist
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=i ** (i - 2))))[-1]
def A308520_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (
blist := tuple(accumulate(reversed(blist), initial=i * (i + 1) // 2 + 1))
)[-1]
def A307593_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m = m * i + 1
def A306880_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=i**i)))[-1]
def A306881_gen(): # generator of terms
yield 0
blist = (0,)
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=i ** (i - 1))))[-1]
def A296792_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1, 2):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= i
def A347072_gen(): # generator of terms
blist, m = (0,), 1
yield from blist
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= i
def A307879_gen(): # generator of terms
blist, m = tuple(), 1
yield from blist
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 4
def A307878_gen(): # generator of terms
blist, m = tuple(), 1
yield from blist
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 3
def A306836_gen(): # generator of terms
blist, a, b = (1,), 1, 1
yield from blist
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=b)))[-1]
a, b = b, (b * (2 * i + 1) + (3 * i - 3) * a) // (i + 2)
def A306832_gen(): # generator of terms
blist, a, b = (1,), 1, 1
yield from blist
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=b)))[-1]
a, b = b, (b * (2 * i - 1) + (3 * i - 3) * a) // i
def A231894_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c = c * (4 * i + 2) // (i + 2)
def A000736_gen(): # generator of terms
yield 1
blist, c = (1,), 1
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c = c * (4 * i + 2) // (i + 2)
def A230961_gen(): # generator of terms
blist, m = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=(m := m * i))))[-1]
def A231200_gen(): # generator of terms
blist = tuple()
for i in count(0, 2):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
def A092090_gen(): # generator of terms
blist, a, b = tuple(), 1, 2
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
a, b = b, a + b
def A062161_gen(): # generator of terms
blist, m = tuple(), 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=(m := 1 - m))))[-1]
def A062272_gen(): # generator of terms
blist, m = tuple(), 0
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=(m := 1 - m))))[-1]
def A000744_gen(): # generator of terms
blist, a, b = tuple(), 1, 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=a)))[-1]
a, b = b, a + b
def A000660_gen(): # generator of terms
yield 1
blist = (1,)
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
def A000733_gen(): # generator of terms
yield 1
blist = (1,)
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=npartitions(i))))[-1]
def A000737_gen(): # generator of terms
blist = tuple()
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
def A000734_gen(): # generator of terms
yield 1
blist, m = (1,), 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 2
def A000751_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=npartitions(i))))[-1]
def A000754_gen(): # generator of terms
blist = tuple()
for i in count(1, 2):
yield (blist := tuple(accumulate(reversed(blist), initial=i)))[-1]
def A000732_gen(): # generator of terms
yield 1
blist = (1,)
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=prime(i))))[-1]
def A000697_gen(): # generator of terms
yield 1
blist, m = (1,), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m += 2 * i + 1
def A000752_gen(): # generator of terms
blist, m = tuple(), 1
while True:
yield (blist := tuple(accumulate(reversed(blist), initial=m)))[-1]
m *= 2
def A230953_gen(): # generator of terms
blist = tuple()
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=prime(i))))[-1]
def A230954_gen(): # generator of terms
blist = tuple()
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=composite(i))))[-1]
def A230955_gen(): # generator of terms
yield 1
blist = (1,)
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=composite(i))))[-1]
def A000746_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(2):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c += i
def A000745_gen(): # generator of terms
blist, c = tuple(), 1
for i in count(1):
yield (blist := tuple(accumulate(reversed(blist), initial=c)))[-1]
c += 2 * i + 1
if sys.version_info >= (3, 10):
def A230952_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (blist := tuple(accumulate(reversed(blist), initial=i.bit_count())))[
-1
]
else:
def A230952_gen(): # generator of terms
blist = tuple()
for i in count(0):
yield (
blist := tuple(accumulate(reversed(blist), initial=bin(i).count("1")))
)[-1]
def A000764_gen(): # generator of terms
blist, alist = (1, 2), (1,)
yield from blist
while True:
yield (
blist := tuple(
accumulate(
reversed(blist),
initial=(alist := list(accumulate(alist, initial=alist[-1])))[-1],
)
)
)[-1]
def A182665(n):
if n == 1:
return 0
plist = tuple(p**q for p, q in factorint(n).items())
return (
1
if len(plist) == 1
else n
- int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
def A354921_gen(startvalue=2): # generator of terms
for n in count(max(startvalue, 2)):
plist = tuple(p**q for p, q in factorint(n).items())
if (
len(plist) == 1
or (
n
- int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
& 1
):
yield n
def A354922_gen(startvalue=1): # generator of terms
if startvalue <= 1:
yield 1
for n in count(max(startvalue, 2)):
plist = tuple(p**q for p, q in factorint(n).items())
if (
len(plist) != 1
and not (
n
- int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
& 1
):
yield n
def A354920(n):
if n == 1:
return 0
plist = tuple(p**q for p, q in factorint(n).items())
return (
1
if len(plist) == 1
else (
n
- int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
)
& 1
)
def A354919_gen(startvalue=1): # generator of terms
if startvalue <= 1:
yield 1
for n in count(max(startvalue, 2)):
plist = tuple(p**q for p, q in factorint(n).items())
if len(plist) == 1:
if (n - 1) & 1:
yield n
elif (
int(
min(
min(crt((m, n // m), (0, -1))[0], crt((n // m, m), (0, -1))[0])
for m in (
prod(d)
for l in range(1, len(plist) // 2 + 1)
for d in combinations(plist, l)
)
)
)
& 1
):
yield n
def A068311(n):
return (
sum(
(
factorial(n) * e // p
for p, e in sum(
(Counter(factorint(m)) for m in range(2, n + 1)),
start=Counter({2: 0}),
).items()
)
)
if n > 1
else 0
)
def A068327(n):
return sum((n ** (n + 1) * e // p for p, e in factorint(n).items())) if n > 1 else 0
def A168386(n):
return (
sum(
(
factorial2(n) * e // p
for p, e in sum(
(Counter(factorint(m)) for m in range(n, 1, -2)),
start=Counter({2: 0}),
).items()
)
)
if n > 1
else 0
)
def A260620(n):
s = prod(factorial(i) for i in range(2, n + 1))
return (
sum(
s * e // p
for p, e in sum(
(
(lambda x: Counter({k: x[k] * (n - m + 1) for k in x}))(
factorint(m)
)
for m in range(2, n + 1)
),
start=Counter({2: 0}),
).items()
)
if n > 1
else 0
)
def A260619(n):
s = prod(i**i for i in range(2, n + 1))
return (
sum(
s * e // p
for p, e in sum(
(
(lambda x: Counter({k: x[k] * m for k in x}))(factorint(m))
for m in range(2, n + 1)
),
start=Counter({2: 0}),
).items()
)
if n > 1
else 0
)
def A068329(n):
f = fibonacci(n)
return sum((f * e // p for p, e in factorint(f).items())) if n > 2 else 0
|
from matplotlib import pyplot
import numpy
import sys
import os
def plot_nx(length_frequencies, total_length, output_dir):
figure = pyplot.figure()
axes = pyplot.axes()
legend_names = list()
x1 = 0
y_prev = None
x_coords = list()
y_coords = list()
for length,frequency in length_frequencies:
for i in range(frequency):
y = length
width = float(length) / float(total_length)
x2 = x1 + width
if y_prev is not None:
x_coords.extend([x1, x1])
y_coords.extend([y_prev, y])
x_coords.extend([x1, x2])
y_coords.extend([y, y])
x1 = x2
y_prev = y
if y_coords[-1] != 0:
y_coords.append(0)
x_coords.append(x_coords[-1])
axes.plot(x_coords, y_coords, linewidth=0.6)
axes.axvline(0.5, linestyle="--", alpha=0.3, linewidth=0.7, zorder=-1)
axes.set_xlim([0, 1])
axes.set_title("Nx")
axes.set_xlabel("Cumulative coverage (normalized to 1)")
axes.set_ylabel("Length")
path = os.path.join(output_dir, "Nx.svg")
sys.stderr.write("SAVING FIGURE: %s\n" % path)
figure.savefig(path, dpi=200)
pyplot.close()
def plot_iterative_histogram(iterative_histogram, output_dir):
figure = pyplot.figure()
axes = pyplot.axes()
bounds = numpy.array(iterative_histogram.edges)
center = (bounds[:-1] + bounds[1:]) / 2
axes.bar(center, iterative_histogram.histogram, width=iterative_histogram.bin_size, align="center")
axes.set_xlabel("Read length (bp)")
axes.set_ylabel("Frequency")
path = os.path.join(output_dir, "histogram.svg")
sys.stderr.write("SAVING FIGURE: %s\n" % path)
figure.savefig(path, dpi=200)
pyplot.close()
|
from ..parents import ConnRDBMS
from ..parents import DB as ParentDB
import sqlalchemy
import sys
import os
import logging as lg
import jaydebeapi
import pprint
lg.basicConfig()
logging = lg.getLogger(__name__)
class DB(ConnRDBMS, ParentDB):
# https://stackoverflow.com/questions/25596737/working-with-an-access-database-in-python-on-non-windows-platform-linux-or-mac
#sql_alchemy_uri ='access:///{file_path}'
sql_alchemy_uri = None
ucanaccess_jars = [
"./jdbc_jar/ucanaccess-4.0.2.jar",
"./jdbc_jar/commons-lang-2.6.jar",
"./jdbc_jar/commons-logging-1.1.3.jar",
"./jdbc_jar/hsqldb-2.3.1.jar",
"./jdbc_jar/jackcess-2.1.6.jar",
]
classpath = ":".join(os.path.abspath(os.path.join(
os.path.dirname(__file__), i)) for i in ucanaccess_jars)
# https://dev.mysql.com/doc/refman/8.0/en/environment-variables.html
def __init__(self, file_path, autocommit=None,loglevel=None):
logging.level=loglevel
self.file_path = os.path.abspath(file_path)
self.autocommit = autocommit
# need to set this for attempting connection
self.str = 'DB: MSAccess:{}:autocommit={}'.format(
file_path, self.autocommit)
self.conn = jaydebeapi.connect(
"net.ucanaccess.jdbc.UcanaccessDriver",
"jdbc:ucanaccess://{file_path};".format(file_path=self.file_path),
["", ""],
self.classpath
)
self.cursor = None
def connect_SqlAlchemy(self):
raise Exception('sqlAlchemy not supported for MSAccess')
def get_all_tables(self):
results = self.conn.jconn.getMetaData().getTables(None, None, "%", None)
table_reader_cursor = self.conn.cursor()
table_reader_cursor._rs = results
table_reader_cursor._meta = results.getMetaData()
read_results = table_reader_cursor.fetchall()
return [row[2] for row in read_results if row[3] == 'TABLE']
|
import collections
from zope.interface import implementer
from sqlalchemy import (
Column,
String,
Unicode,
Integer,
Float,
ForeignKey,
)
from sqlalchemy.orm import relationship, backref
from uritemplate import expand, variables
from clld import interfaces
from clld.db.meta import CustomModelMixin, Base
from clld.db.models.common import Contribution, Parameter, Value, IdNameDescriptionMixin, Unit
from clld.lib.rdf import url_for_qname, NAMESPACES
from clldutils.misc import lazyproperty
# Maximum number of language columns to display for a conceptlist:
MAX_LANG_COLS = 4
# -----------------------------------------------------------------------------
# specialized common mapper classes
# -----------------------------------------------------------------------------
@implementer(interfaces.IValue)
class Concept(CustomModelMixin, Value):
pk = Column(Integer, ForeignKey('value.pk'), primary_key=True)
number = Column(Integer)
number_suffix = Column(String)
@property
def label(self):
comps = self.name.split('; ')
res = comps[0]
if len(comps) > 1:
res += '…'
return res
def __rdf__(self, request):
yield 'rdf:type', url_for_qname('skos:Concept')
yield 'skos:topConceptOf', request.resource_url(self.valueset.contribution)
@property
def glossdict(self):
return {gl.lang_key: gl.name for gl in self.glosses}
@implementer(interfaces.IUnit)
class Gloss(CustomModelMixin, Unit):
pk = Column(Integer, ForeignKey('unit.pk'), primary_key=True)
lang_key = Column(Unicode)
concept_pk = Column(Integer, ForeignKey('concept.pk'))
concept = relationship(Concept, backref=backref('glosses'))
@implementer(interfaces.IParameter)
class ConceptSet(CustomModelMixin, Parameter):
pk = Column(Integer, ForeignKey('parameter.pk'), primary_key=True)
semanticfield = Column(Unicode)
ontological_category = Column(Unicode)
representation = Column(Integer)
def __rdf__(self, request):
yield 'dcterms:type', self.ontological_category
yield 'rdf:type', url_for_qname('skos:Collection')
for vs in self.valuesets:
yield 'skos:member', request.resource_url(vs.values[0])
for rel in self.rel_to:
if rel.description == 'broader':
yield 'skos:broader', request.resource_url(rel.target)
elif rel.description == 'narrower':
yield 'skos:narrower', request.resource_url(rel.target)
else:
yield 'skos:related', request.resource_url(rel.target)
for rel in self.rel_from:
if rel.description == 'broader':
yield 'skos:narrower', request.resource_url(rel.source)
elif rel.description == 'narrower':
yield 'skos:broader', request.resource_url(rel.source)
else:
yield 'skos:related', request.resource_url(rel.source)
for meta in self.meta:
if meta.propertyUrl and meta.valueUrl:
yield meta.propertyUrl, meta.valueUrl
class MetaProvider(Base, IdNameDescriptionMixin):
url = Column(String)
@property
def schema(self):
d = collections.OrderedDict()
for c in self.jsondata['tableSchema']['columns']:
d[c['name']] = c
return d
class ConceptSetMeta(Base, IdNameDescriptionMixin):
metaprovider_pk = Column(Integer, ForeignKey('metaprovider.pk'))
conceptset_pk = Column(Integer, ForeignKey('conceptset.pk'))
metaprovider = relationship(MetaProvider, backref='meta')
conceptset = relationship(
ConceptSet,
backref=backref('meta', order_by=[metaprovider_pk]))
key = Column(Unicode)
value = Column(Unicode)
@lazyproperty
def schema(self):
return self.metaprovider.schema[self.key]
@lazyproperty
def propertyUrl(self):
url = self.schema.get('propertyUrl')
if url and ':' in url and url.split(':', 1)[0] in NAMESPACES:
return url
@lazyproperty
def valueUrl(self):
url = self.schema.get('valueUrl')
if url and variables(url) == {self.key}:
return expand(url, {self.key: self.value})
class Relation(Base):
source_pk = Column(Integer, ForeignKey('parameter.pk'))
target_pk = Column(Integer, ForeignKey('parameter.pk'))
description = Column(Unicode)
source = relationship(ConceptSet, foreign_keys=[source_pk], backref='rel_to')
target = relationship(ConceptSet, foreign_keys=[target_pk], backref='rel_from')
class Tag(Base, IdNameDescriptionMixin):
pass
@implementer(interfaces.IContribution)
class Conceptlist(CustomModelMixin, Contribution):
pk = Column(Integer, ForeignKey('contribution.pk'), primary_key=True)
source_languages = Column(Unicode)
target_languages = Column(Unicode)
items = Column(Integer)
uniqueness = Column(Float)
year = Column(Integer)
alias = Column(Unicode)
@property
def source_languages_list(self):
return [s.lower() for s in self.source_languages.split()]
@property
def excess_source_languages(self):
return len(self.source_languages_list) > MAX_LANG_COLS
def __rdf__(self, request):
yield 'rdf:type', url_for_qname('skos:ConceptScheme')
for vs in self.valuesets:
yield 'skos:hasTopConcept', request.resource_url(vs.values[0])
for ref in self.references:
yield 'dcterms:source', request.resource_url(ref.source)
@property
def github_url(self):
return 'https://github.com/concepticon/concepticon-data/blob/master' \
'/concepticondata/conceptlists/{0}.tsv'.format(self.id)
@property
def tags(self):
return [ta.tag for ta in self.tag_assocs]
class ConceptlistTag(Base):
conceptlist_pk = Column(Integer, ForeignKey('conceptlist.pk'))
tag_pk = Column(Integer, ForeignKey('tag.pk'))
conceptlist = relationship(Conceptlist, backref='tag_assocs')
tag = relationship(Tag, backref='conceptlist_assocs')
|
idade=int(input('Digite sua idade: '))
if idade<16:
print('Não pode votar')
elif idade>=18 and idade<=70:
print('Você é obrigado a votar')
else:
print('Seu voto é opcional') |
import os
_current_dir = os.path.abspath(os.path.dirname(__file__))
PT_HOME = os.path.normpath(os.path.join(_current_dir, "../../../.."))
PT_VERSION = '0.01'
|
"""
Usage: plotAtmFlux.py [-o OUTPUT_FILE] -p PARAMETER_FILE -f FLUX_FILE
Options:
-h --help Help.
-o --output_file OUTPUT_FILE Output file.
-p --parameter_file PARAMETER_FILE Input file.
-f --flux_file FLUX_FILE Flux file.
"""
from docopt import docopt
from pathlib import Path
from fiesta import nuFlux as nf
from fiesta import tools as tls
from scipy.optimize import curve_fit
from os.path import exists
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import json
def main():
arguments = docopt(__doc__)
if (arguments['--output_file']==None):
arguments['--output_file']=Path(arguments['--flux_file']).stem+'.png'
with open(arguments["--parameter_file"], 'r') as json_file:
p = json.load(json_file)
json_file.close()
flux=nf.read_flux_file(arguments["--flux_file"])
phi=1.66
gamma=2.53
e0=100e3
c0=3e-18
fig1, axs1 = plt.subplots(2, 2)
fig1.set_size_inches(10,7)
# panel 1: electron neutrinos
axs1[0, 0].plot(flux["E"], flux["nu_e"], color='darkorange', label='atmospheric')
axs1[0, 0].plot(flux["E"][600:],
nf.atmospheric_flux(flux["E"][600:], p["nu_e"]["phi"], p["nu_e"]["gamma"]),
color='grey', label='fit')
axs1[0, 0].set_title(r'$\nu_{e}$')
# panel 2: muon neutrinos
axs1[0, 1].plot(flux["E"], flux["nu_mu"], color='darkorange', label='atmospheric')
axs1[0, 1].plot(flux["E"][600:],
nf.atmospheric_flux(flux["E"][600:], p["nu_mu"]["phi"], p["nu_mu"]["gamma"]),
color='grey', label='fit')
axs1[0, 1].set_title(r'$\nu_{\mu}$')
# panel 3: electron antineutrinos
axs1[1, 0].plot(flux["E"], flux["nu_e_bar"], color='darkorange', label='atmospheric')
axs1[1, 0].plot(flux["E"][600:],
nf.atmospheric_flux(flux["E"][600:], p["nu_e_bar"]["phi"], p["nu_e_bar"]["gamma"]),
color='grey', label='fit')
axs1[1, 0].set_title(r'$\bar{\nu}_{e}$')
# panel 4: muon antineutrinos
axs1[1, 1].plot(flux["E"], flux["nu_mu_bar"], color='darkorange', label='atmospheric')
axs1[1, 1].plot(flux["E"][600:],
nf.atmospheric_flux(flux["E"][600:], p["nu_mu_bar"]["phi"], p["nu_mu_bar"]["gamma"]),
color='grey', label='fit')
axs1[1, 1].set_title(r'$\bar{\nu}_{\mu}$')
# general settings for all the panels
for ax in [axs1[1, 0], axs1[1, 1]]:
ax.set(xlabel='log10(E/GeV)')
for ax in [axs1[0, 0], axs1[1, 0]]:
ax.set(ylabel=r'F$_{\nu}$/($GeV ^{-1} \cdot cm ^{-2}\cdot s ^{-1}\cdot sr ^{-1}$)')
for ax in axs1.flatten():
ax.grid()
ax.plot(flux["E"], nf.astro_flux(flux["E"], phi, gamma, e0, c0)/6,
color='royalblue', label='astro')
ax.legend()
ax.set_yscale('log')
ax.set_xscale('log')
# figure showing all fluxes. The astro flux, is the total one (i.e. we don't divide by 6 to get the individual contributions)
log_Emin = 2.0
log_Emax = 12.0
nPoints = 2000
step=(log_Emax-log_Emin)/nPoints
logE=np.arange(log_Emin, log_Emax, step)
fig2, axs2 = plt.subplots(1,2)
fig2.set_size_inches(11,4)
# astro
axs2[0].plot(np.power(10,logE), nf.astro_flux(np.power(10,logE), phi, gamma, e0, c0)/6, color='royalblue', label=r'astro $\nu _{i}$', linewidth=2)
axs2[1].plot(np.power(10,logE), nf.astro_flux(np.power(10,logE), phi, gamma, e0, c0), color='royalblue', label=r'astro total', linewidth=2, alpha=1)
# atm nu_e fit
axs2[0].plot(np.power(10,logE)[700:],
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_e"]["phi"], p["nu_e"]["gamma"]),
color='darkorange', linestyle='--', alpha=0.7)
# atm nu_e data
axs2[0].plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_e"]["phi"], p["nu_e"]["gamma"]),
color='darkorange', linestyle='-', alpha=1, label=r'$\nu_{e}$')
# atm nu_mu fit
axs2[0].plot(np.power(10,logE)[700:],
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_mu"]["phi"], p["nu_mu"]["gamma"]),
color='limegreen', linestyle='--', alpha=0.7)
# atm nu_mu data
axs2[0].plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_mu"]["phi"], p["nu_mu"]["gamma"]),
color='limegreen', linestyle='-', alpha=1, label=r'$\nu_{\mu}$')
# atm nu_e_bar fit
axs2[0].plot(np.power(10,logE)[700:],
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_e_bar"]["phi"], p["nu_e_bar"]["gamma"]),
color='red', linestyle='--', alpha=0.7)
# atm nu_e_bar data
axs2[0].plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_e_bar"]["phi"], p["nu_e_bar"]["gamma"]),
color='red', linestyle='-', alpha=1, label=r'$\bar{\nu}_{e}$')
# atm nu_mu_bar fit
axs2[0].plot(np.power(10,logE)[700:],
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_mu_bar"]["phi"], p["nu_mu_bar"]["gamma"]),
color='olivedrab', linestyle='--', alpha=0.7)
# atm nu_mu_bar data
axs2[0].plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_mu_bar"]["phi"], p["nu_mu_bar"]["gamma"]),
color='olivedrab', linestyle='-', alpha=1, label=r'$\bar{\nu}_{\mu}$')
# atm total data
axs2[1].plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_e"]["phi"], p["nu_e"]["gamma"])+
nf.atmospheric_flux(flux["E"][:800], p["nu_mu"]["phi"], p["nu_mu"]["gamma"])+
nf.atmospheric_flux(flux["E"][:800], p["nu_e_bar"]["phi"], p["nu_e_bar"]["gamma"])+
nf.atmospheric_flux(flux["E"][:800], p["nu_mu_bar"]["phi"], p["nu_mu_bar"]["gamma"]),
color='darkorange', linestyle='-', linewidth=2, alpha=1, label=r'atmospheric')
# atm total fit
axs2[1].plot(np.power(10,logE)[700:],
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_e"]["phi"], p["nu_e"]["gamma"])+
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_mu"]["phi"], p["nu_mu"]["gamma"])+
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_e_bar"]["phi"], p["nu_e_bar"]["gamma"])+
nf.atmospheric_flux(np.power(10,logE)[700:], p["nu_mu_bar"]["phi"], p["nu_mu_bar"]["gamma"]),
color='darkorange', linestyle='--', linewidth=2, alpha=1)
for ax in [axs2[0], axs2[1]]:
ax.set(xlabel='log10(E/GeV)')
ax.set_yscale('log')
ax.set_xscale('log')
ax.grid()
ax.legend()
for ax in [axs2[0]]:
ax.set(ylabel=r'F$_{\nu}$/($GeV ^{-1} \cdot cm ^{-2}\cdot s ^{-1}\cdot sr ^{-1}$)')
fig3, axs3 = plt.subplots()
# astro
axs3.plot(np.power(10,logE), nf.astro_flux(np.power(10,logE), phi, gamma, e0, c0)/6, color='royalblue', label=r'astro $\nu _{i}$', linewidth=2)
# atm nu_e data
axs3.plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_e"]["phi"], p["nu_e"]["gamma"]),
color='darkorange', linestyle='-', alpha=1, label=r'$\nu_{e}$')
# atm nu_mu data
axs3.plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_mu"]["phi"], p["nu_mu"]["gamma"]),
color='limegreen', linestyle='-', alpha=1, label=r'$\nu_{\mu}$')
# atm nu_e_bar data
axs3.plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_e_bar"]["phi"], p["nu_e_bar"]["gamma"]),
color='red', linestyle='-', alpha=1, label=r'$\bar{\nu}_{e}$')
# atm nu_mu_bar data
axs3.plot(flux["E"][:800],
nf.atmospheric_flux(flux["E"][:800], p["nu_mu_bar"]["phi"], p["nu_mu_bar"]["gamma"]),
color='olivedrab', linestyle='-', alpha=1, label=r'$\bar{\nu}_{\mu}$')
axs3.set_xlim(5e4,5e5)
axs3.set_ylim(1e-21,1e-17)
axs3.set_yscale('log')
axs3.set_xscale('log')
axs3.set(ylabel=r'F$_{\nu}$/($GeV ^{-1} \cdot cm ^{-2}\cdot s ^{-1}\cdot sr ^{-1}$)',xlabel=r'E$_{\nu}/GeV$')
axs3.grid(which='major', linestyle='-')
axs3.grid(which='minor', linestyle='--')
axs3.legend()
fig1.savefig('nu_flux_1.png', dpi=fig1.dpi)
fig2.savefig('nu_flux_2.png', dpi=fig2.dpi)
fig3.savefig('nu_flux_3.png', dpi=fig2.dpi)
plt.show()
if __name__== '__main__':
main()
|
#!/usr/bin/python
import os
import sys
import presquel
import argparse
VERSION = "%{prog}s " + presquel.VERSION_STR
def find_max_order_len(max_len, schema_list):
for sch in schema_list:
if not isinstance(sch, presquel.model.SchemaObject):
raise Exception("expected SchemaObject, found " + repr(sch))
ord_len = len(str(sch.order.items()[0]))
if ord_len > max_len:
max_len = ord_len
max_len = find_max_order_len(max_len, sch.sub_schema)
return max_len
class SourceSetup(object):
def __init__(self, base_dir: str):
self.problems = []
version_split = base_dir.split("@")
if len(version_split) == 1:
self.base_dir = base_dir
self.version_name = None
elif len(version_split) == 2:
self.base_dir = version_split[0]
self.version_name = version_split[1]
else:
self.problems.append(
"invalid version definition: '" + base_dir + "'")
return
self.package_name = os.path.basename(self.base_dir)
if not os.path.isdir(self.base_dir):
self.problems.append("not a directory: " + self.base_dir)
self.out_dir = None
self.package = None
self.branch = None
def load(self):
self.package = presquel.load_package(self.base_dir, self.package_name)
for number in self.package.unresolved_branch_versions:
self.problems.append(
"package references unknown version number " + str(number))
self.package_name = self.package.package
if self.version_name is None:
self.branch = self.package.get_newest_version()
if self.branch is None:
self.problems.append("no versions in package")
else:
for version in self.package.get_versions():
if version.is_version(self.version_name):
self.branch = self.package.get_version(version)
break
if self.branch is None:
self.problems.append(
"could not find version '" + self.version_name +
"' in package; available versions are '" +
"', '".join([
str(ver) for ver in self.package.get_versions()]) +
"'"
)
if self.branch is not None:
self.problems.extend(
[str(branch) for branch in self.branch.schema_version.problems])
def set_output(self, output_dir: str, directories: bool, force: bool):
if directories:
output_dir = os.path.join(output_dir, self.package_name)
if os.path.exists(output_dir) and not os.path.isdir(output_dir):
self.problems.append("output directory '" + output_dir +
"' exists but is not a directory")
elif os.path.isdir(output_dir) and not force:
self.problems.append("output directory '" + output_dir +
"' exists but force flag not set; will not " +
"overwrite")
else:
self.out_dir = output_dir
if __name__ == '__main__':
parser = argparse.ArgumentParser(fromfile_prefix_chars='@')
parser.add_argument('--version', action='version', version=VERSION)
parser.add_argument("-v", "--verbose",
help="increase output verbosity",
action="store_true")
parser.add_argument("-f", "--force",
help="overwrite any existing data",
action="store_true")
parser.add_argument("-o", "--output",
help="directory to store the generated files",
action="store",
required=True)
parser.add_argument("-d", "--directories",
help="""put each source directory into its own named
sub-directory under the output directory""",
action="store_true")
parser.add_argument("-p", "--platform",
help="SQL platform to generate for",
action="store",
required=True)
parser.add_argument('sources', metavar='source', nargs='+',
help="""source directory to use an input. By default,
this will pull in the highest version number to
generate. To generate one specific version, use the
format 'source/dir/name@1.2.3' to generate version 1.2.3
from the source directory source/dir/name.""")
arg_values = parser.parse_args()
gens = presquel.get_generator(arg_values.platform)
if len(gens) <= 0:
print("No generator found for " + arg_values.platform)
sys.exit(1)
gen = gens[0]
sources = []
problems = False
for source in arg_values.sources:
setup = SourceSetup(source)
setup.load()
setup.set_output(arg_values.output, arg_values.directories,
arg_values.force)
if len(setup.problems) > 0:
problems = True
print("Problems discovered for " + source + ":")
for problem in setup.problems:
print("[" + source + "] " + str(problem))
else:
sources.append(setup)
if problems:
sys.exit(1)
for setup in sources:
assert isinstance(setup, SourceSetup)
os.makedirs(setup.out_dir)
branch_version = setup.branch.schema_version
order_length = find_max_order_len(-1, branch_version.schema)
name_format = ('{0:0' + str(order_length) + 'd}_{1}.sql')
for schema in branch_version.schema:
filename = os.path.join(
setup.out_dir, name_format.format(
schema.order.items()[0], schema.name))
print("Generating " + filename)
with open(filename, 'w') as f:
for script in gen.generate_base(schema):
f.write(script)
|
import sys
sys.path.append('..')
from booru_db import BooruDatabase
from database import *
import datetime
import json
import traceback
import random
import time
import logging
import redis
import collections
r = redis.Redis(db=12)
bdb = BooruDatabase('danbooru')
def parse_date(val):
try:
v = datetime.datetime.strptime(val, '%Y-%m-%d %H:%M:%S %Z')
except:
val = val.split(' ')
val[1] = val[1] + '0'
val = ' '.join(val)
v = datetime.datetime.strptime(val, '%Y-%m-%d %H:%M:%S.%f %Z')
if v == datetime.datetime(1970, 1, 1, 0, 0):
return None
return v
def insert_row(struct, skip_if_exists=False):
print(struct['id'])
post = Post()
post_existing = bdb.post[ int(struct['id']) ]
if skip_if_exists and (post_existing is not None):
return None
if post_existing:
post = post_existing
#print(post, post.__data__, flush=True)
post.local_id = struct['id']
#print(post.post_created_at, parse_date(struct['created_at']))
#print(post.post_updated_at, parse_date(struct['updated_at']))
#input()
post.post_created_at = parse_date(struct['created_at'])
post.post_updated_at = parse_date(struct['updated_at'])
post.row_updated_at = datetime.datetime.now()
post.rating = struct['rating']
post.source = struct['source'] or None
post.score = struct['score']
post.parent_local_id = int(struct['parent_id']) or None
post.uploaded_by = User.get_or_create(board=bdb.booru, local_id=int(struct['uploader_id']))[0]
bdb.post[ int(struct['id']) ] = post
post = bdb.post[ int(struct['id']) ]
#print(post, post.__data__, flush=True)
old_tags = sorted(bdb.tag[post])
new_tags = sorted([tag['name'] for tag in struct['tags']])
if old_tags != new_tags:
#print('updating tag set', old_tags, new_tags)
bdb.tag[post] = new_tags
else:
pass
#print('skipped tag set')
postfavs_existing = set( [i[0] for i in PostFavs.select(User.local_id).join(User).where(PostFavs.post==post).tuples()] )
postfavs_new = set([int(i) for i in struct['favs']])
diff_set = postfavs_existing.symmetric_difference(postfavs_new)
if diff_set:
#print('fav set difference so updating', postfavs_existing, '->', postfavs_new)
fav_users = dict()
for i in User.select().where(User.board == bdb.booru).where(User.local_id.in_([int(i) for i in struct['favs']])):
fav_users[i.local_id] = i
PostFavs.delete().where(PostFavs.post == post).execute()
postfavs_list = []
for fav in struct['favs']:
fav = int(fav)
if fav not in fav_users:
fav_users[fav] = User.get_or_create(board=bdb.booru, local_id=int(fav))[0]
postfavs_list.append(PostFavs(post=post, user=fav_users[fav]))
PostFavs.bulk_create(postfavs_list)
danpost = DanbooruPostMetadata.get_or_none(post=post) or DanbooruPostMetadata(post=post)
#print(danpost.__data__)
danpost.up_score = int(struct['up_score'])
danpost.down_score = int(struct['up_score'])
danpost.pixiv_id = int(struct['pixiv_id']) or None
danpost.approved_by = User.get_or_create(board=bdb.booru, local_id=int(struct['approver_id']))[0]
danpost.is_pending = struct['is_pending']
danpost.is_flagged = struct['is_flagged']
danpost.is_deleted = struct['is_deleted']
danpost.is_banned = struct['is_banned']
danpost.is_status_locked = struct['is_status_locked']
danpost.is_note_locked = struct['is_note_locked']
try:
danpost.save(force_insert=True)
except IntegrityError:
danpost.save()
imgpost = ImageMetadata.get_or_none(post=post) or ImageMetadata(post=post)
#print(imgpost.__data__)
imgpost.image_width = int(struct['image_width'])
imgpost.image_height = int(struct['image_height'])
imgpost.file_size = int(struct['file_size'])
imgpost.md5 = struct['md5']
try:
imgpost.save(force_insert=True)
except IntegrityError:
imgpost.save()
def insert_row_atomic(*args, **kwargs):
with db.atomic():
return insert_row(*args, **kwargs)
#insert_row_atomic(json.loads(input()))
class CountHandler(logging.Handler):
def __init__(self):
self.count = 0
super().__init__()
def emit(self, record):
self.count += 1
def handle(self, record):
self.count += 1
def reset(self):
self.count = 0
counter = CountHandler()
logger = logging.getLogger('peewee')
logger.addHandler(counter)
logger.setLevel(logging.DEBUG)
class DanbooruDumpRow(MyModel):
post_id = IntegerField()
content = TextField()
DANBOORU = Imageboard.get(name='danbooru')
POST_ENTITY, _ = EntityType.get_or_create(name='post')
when = time.time()
#for row in DanbooruDumpRow.select().order_by(fn.Rand()):
def infinite_counter():
i = 0
while 1:
i += 1
yield i
start = time.time()
try:
start_times = collections.deque(maxlen=50)
to_delete = collections.deque()
for ind in db.batch_commit(infinite_counter(), 100):
# count = DanbooruDumpRow.select(fn.COUNT(DanbooruDumpRow.id)).scalar()
# if not count:
# print('All done!!!')
# break
# row = DanbooruDumpRow.select().where(DanbooruDumpRow.id >= random.randint(0, count)).get()
start_times.append(time.time())
rid = r.randomkey()
row = r.get(rid)
# print('selecting row', rid, 'took', time.time()-when, 'seconds and', counter.count, 'queries')
when = time.time()
insert_row_atomic(json.loads(row))
print('inserting took', time.time()-when, 'seconds and', counter.count, 'queries')
when = time.time()
ImportedEntity.get_or_create(entity_type=POST_ENTITY, board=DANBOORU, entity_local_id=rid, final=False)
to_delete.append(rid)
while len(to_delete) > 500:
v = to_delete.popleft()
print('deleting from redis', v)
r.delete(v)
# print('removing took', time.time()-when, 'seconds and', counter.count, 'queries')
counter.reset()
when = time.time()
print('Current rate:', len(start_times) / (when - start_times[0]))
print()
except KeyboardInterrupt:
input('Stopped, enter to continue or another ^C to quit')
|
'''Extracts the texts of a scraped LexDk corpus.
Usage:
python extract_lexdk_texts.py <lexdk_jsonl_dump>
'''
import sys
import json
from pathlib import Path
from tqdm.auto import tqdm
def main():
file_in = Path(sys.argv[1])
file_out = file_in.parent / f'{file_in.stem}.txt'
with file_out.open('w', encoding='utf-8') as f_out:
with file_in.open('r', encoding='utf-8') as f_in:
desc = f'Extracting texts from {file_in}'
for line in tqdm(f_in, desc=desc):
data = json.loads(line)
f_out.write(data['text'])
if __name__ == '__main__':
main()
|
'''
By Chris Paxton
Copyright (c) 2017, The Johns Hopkins University
All rights reserved. See license for details.
'''
from abstract import AbstractExtract
import operator
'''
Return the most visited nodes all the way down the tree.
'''
class MostVisitedExtract(AbstractExtract):
def __call__(self, node):
nodes = [node]
while not node.terminal and len(node.children) > 0:
visits = [(i, child.n_visits)
for (i, child) in enumerate(node.children)]
max_idx, max_num_visits = max(visits, key=operator.itemgetter(1))
node = node.children[max_idx]
nodes.append(node)
return nodes
'''
Return the most visited nodes all the way down the tree.
If some branches have negative expected reward, we want to ignore those -- it
does not matter how many times we visited them.
'''
class MostVisitedPositiveExtract(AbstractExtract):
def __call__(self, node):
nodes = [node]
while not node.terminal and len(node.children) > 0:
if max([child.avg_reward for child in node.children]) > 0:
allowed = lambda child: child.avg_reward > 0
else:
allowed = lambda child: True
visits = [(i, child.n_visits)
for (i, child) in enumerate(node.children) if allowed(child)]
max_idx, max_num_visits = max(visits, key=operator.itemgetter(1))
node = node.children[max_idx]
nodes.append(node)
return nodes
'''
Extract children with the highest average reward.
'''
class HighestAverageRewardExtract(AbstractExtract):
def __call__(self, node):
nodes = [node]
while not node.terminal and len(node.children) > 0:
reward = [(i, child.avg_reward)
for (i, child) in enumerate(node.children)]
if len(reward) == 0:
break
max_idx, max_rewar = max(reward, key=operator.itemgetter(1))
node = node.children[max_idx]
nodes.append(node)
return nodes
|
from collections import OrderedDict
from qtpy.QtGui import QStandardItemModel, QStandardItem
from qtpy.QtCore import Qt
from qtpy.QtWidgets import (QTableView, QWidget, QLabel, QStyledItemDelegate,
QHBoxLayout, QVBoxLayout, QMessageBox,
QPushButton)
from .widgets import MText, vstacked_label
class MTableItemDelegate(QStyledItemDelegate):
"""A ``QStyledItemDelegate`` for use with MTableInterfaceWidgets.
This adds custom ``displayText``, ``setEditorData`` and ``setModelData``
methods that work with the ``mily.widgets`` API. Namely, using the
``get_parameters`` and ``set_default`` methods for reading/writing
to/from the editor widgets. It has a ``self.editor_map`` attribute that
maps the column names to editor widgets. It also has a custom method for
``self.createEditor`` that uses ``self.editor_map`` and returns the
correct editor on request. If editor_map is empty it uses an ``MText``
widget for all columns. It also enforces the inclusion of a parent
attribute (something that is optional in the ``QStyledItemDelegate``) and
adds an ``_name`` attribute for consistency with the `mily.widgets`` API.
"""
def __init__(self, parent, name, *args, editor_map={}, **kwargs):
self._name = name
super().__init__(*args, parent=parent, **kwargs)
self.editor_map = editor_map
def displayText(self, value, locale):
"""Converts the value of the editor to a display string.
This method is called whenever the associated model value is updated,
and updates the associated TableView with the returned str_val for
display. It is written such that it will find the best str to associate
with the object, and will recursively change dict and list keys/items.
"""
def _get_display_str(value):
"""Recursively find a list of attr names for a DisplayText.
This checks a number of attr names to see if any are present and
can be used to give a displayText value. Otherwise it returns the
str generated using ``str(value)``. It will recursively search
``dict`` and ``list`` values and return str(dict) or str(list)
after setting displayText's for each key+value (for dicts) or item
(for lists).
"""
if isinstance(value, list): # recursively treat lists
list_val = []
for item in value:
list_val.append(_get_display_str(item))
str_val = str(list_val).replace('"', '').replace("'", "")
elif isinstance(value, dict): # recursively treat dicts
dict_val = {}
for key, val in value.items():
dict_val[_get_display_str(key)] = _get_display_str(val)
str_val = str(dict_val).replace('"', '').replace("'", "")
else: # check individual values
# Check a list of attrs that can return displayText values.
for attr in ['name', '_name', '__name__']:
str_val = getattr(value, attr, None)
if str_val:
break
# If none of the above worked
if not str_val:
str_val = str(value)
return str_val
return _get_display_str(value)
def setEditorData(self, editor, index):
"""Sets the model data to the editor.
This method is called whenever the editor is opened and sets the
current value of the editor to that in the model. The change here is to
use the ``mily.widget`` API ``editor.set_default(value)`` method. It
also ensures that data associated with the "display" role in the model
is used, which leads to a consistent approach with the
``self.setModelData(...)`` method.
"""
row = index.row()
column = index.column()
try:
value = index.model().item(row, column).data(Qt.DisplayRole)
except AttributeError:
value = None
editor.set_default(value)
def setModelData(self, editor, model, index):
"""Sets the editor data to the model.
This method is called whenever the editor is closed _and_ a change has
been made to the editor value. The change here is to ensure the use of
the ``mily.widget`` API ``editor.get_parameter()`` method to extract
the data from the editor. It then writes the data to the model,
associating it with the "display" role for consistency with the
``self.setEditorData(...)`` method.
It further calls the ``model.update_coupled_parameters`` method to
see if there are any coupled parameters that also need to be updated.
This method takes in a dict mapping column names to new values, a dict
mapping column_names to old values for the entire row and the row
number as inputs and is expected to return a dict mapping column names
to new values for any columns to update in the given row. If
``model.update_coupled_parameters`` is ``None`` it just updates the
value defined by index.
"""
column_names = list(self.parent().editor_map.keys())
# create a dict mapping the column_name to the value to be updated
new_value = editor.get_parameters()[editor._name]
requested_parameters = {column_names[index.column()]: new_value}
row = index.row()
if model.update_coupled_parameters:
# step through each column adding the value to parameters
current_parameters = {}
for column in range(0, model.columnCount()):
item = model.item(row, column)
if item:
value = item.data(Qt.DisplayRole)
else:
value = None
current_parameters[column_names[column]] = value
# call the function to get a new list of coupled values to update.
new_parameters = model.update_coupled_parameters(
requested_parameters, current_parameters, index.row())
for column_name, value in new_parameters.items():
column = column_names.index(column_name)
model.item(row, column).setData(value, Qt.DisplayRole)
else:
model.setData(index, new_value, Qt.DisplayRole)
def createEditor(self, parent, option, index):
"""Creates the editor based on ``self.editor_map``.
This method is whenever a user double clicks on a cell in order to edit
its value. Based on the 'index' argument it works out which key in the
``self.editor_map`` dictionary relates to the cell to be edited, and
creates the editor based on the type defined by the value for that key.
"""
column_name = list(self.editor_map.keys())[index.column()]
editor = self.editor_map.get(column_name, MText)(column_name,
parent=parent)
if editor:
# ensure the editors background is opaque
editor.setAutoFillBackground(True)
# resize the table cell to fit the editor
editor.setMinimumWidth(80)
editor.parent().parent().setRowHeight(index.row(),
editor.height())
editor.parent().parent().setColumnWidth(index.column(),
editor.width())
return editor
class MTableInterfaceView(QTableView):
"""Creates a table view and model for an ``MTableInterfaceWidget``.
This creates a custom QTableView and sets some display options that are
common to ``MTableInterfaceWidget`` tables. It also creates and sets the
model and the delegate to be used in conjunction with this view.
Parameters:
*args/**kwargs : various
args and kwargs to be passed to ``qtpy.QtWidgets.QTableView``.
delegate : QitemDelegate, optional
The ``qtpy.QItemDelegate`` to be associated with the class, default is
the ``MTableItemDelegate``.
model : QStandardItemModel, optional
The ``qtpy.QtGui.QStandardItemModel`` to be associated with the
class, the default is ``qtpy.QtGui.QStandardItemModel.
update_coupled_parameters : func, optional
An optional function that is called every time the data in the model is
updated. It must have the structure:
..code-block:: python
def update_coupled_parameters(requested_parameters,
current_parameters,
row)
...
return new_parameters
where: ``requested_parameters`` is a dict that maps column names to new
requested values, current_parameters is a dict mapping column names to
the current values and row is the model row index (as an int) that is
to be updated. This function should return a dict mapping column names
to values that should be updated.
"""
def __init__(self, parent, name, *args, editor_map={},
delegate=MTableItemDelegate, model=QStandardItemModel,
update_coupled_parameters=None, **kwargs):
self._name = name
self.editor_map = editor_map
super().__init__(*args, parent=parent, **kwargs)
# Apply some style options
self.horizontalHeader().setDefaultAlignment(Qt.AlignHCenter)
self.setAlternatingRowColors(True)
# set the table delegate
self.setItemDelegate(delegate(self, self.parent()._name+'_model',
editor_map=self.editor_map))
# set the model and set column headers from editor_map if possible
self.setModel(model(self))
# add the function for dealing with coupled parameters.
setattr(self.model(),
'update_coupled_parameters',
update_coupled_parameters)
if self.editor_map:
column_names = list(self.editor_map.keys())
self.model().setHorizontalHeaderLabels(column_names)
# resize the table rows/columns to fit the displayText sizes
self.resizeColumnsToContents()
self.resizeRowsToContents()
# resize the table to fit the contents on changes
signals = [self.itemDelegate().closeEditor, self.model().rowsInserted,
self.model().dataChanged]
for signal in signals:
signal.connect(self.resizeColumnsToContents)
signal.connect(self.resizeRowsToContents)
def set_default(self, parameters):
"""Sets the default values from 'parameters' to the model
Sets the data from 'parameters' to the model, overwriting any existing
data in the model. This follows the ``mily.widget`` API.
Parameters
----------
parameters : [dicts]
List of dicts with each dict being a row that maps the column
header to its value.
"""
model = self.model()
# Empty the model.
model.removeRows(0, model.rowCount())
# Add the new data to the model.
for row_params in parameters:
row_data = []
# for each column in the model check if a default is given
for column in range(0, model.columnCount()):
header_item = model.horizontalHeaderItem(column)
header = header_item.text()
item = QStandardItem()
value = row_params.get(header, None)
item.setData(value, Qt.DisplayRole)
row_data.append(item)
model.appendRow(row_data)
def get_parameters(self):
"""Return the entire data from the table.
Returns the entire table data as a list of dicts, with each dict being
a row that maps the column header to it's value. This follows the
``mily.widget`` API.
"""
parameters = []
for row in range(0, self.model().rowCount()):
parameters.append(self.get_row_parameters(row)[self._name])
return {self._name: parameters}
def get_row_parameters(self, row):
"""Returns the data associated with the row defined by 'row'.
Returns the data associated with row as a dictionary mapping column
name to value, and any prefix or suffix data based on the value of the
kwargs prefix and suffix.
Parameters
----------
row : int
The row number who's data should be extracted.
Returns
-------
parameters : dict
A dictionary mapping kwargs to values.
"""
column_names = list(self.editor_map.keys())
model = self.model()
# step through each column adding the value to parameters
parameters = {}
for column in range(0, model.columnCount()):
item = model.item(row, column)
if item:
value = item.data(Qt.DisplayRole)
else:
value = None
parameters[column_names[column]] = value
return {self._name: parameters}
class MTableInterfaceWidget(QWidget):
"""Table like interface widget based on the ``mily`` API.
This widget allows for 'sets' of the same parameters to be defined as rows
in a table. The parameters are defined by the 'keys' in the dictionary
self.table_editor_map, where the values of the dictionary are the widgets
to be used to update the values for the given columns.In addition 2 other
dictionaries ``self.prefix_editor_map`` and ``self.suffix_editor_map`` can
be set in the same way to provide additional 'global' parameters to be
returned by the method ``self.get_parameters()`` or inputted using the
method ``self.set_defaults(...)`` before (prefix) or after (suffix) the
``self.tableView`` data. Prefix parameters appear above the table while
suffix parameters appear below the table.
In addition to the table prefix and suffix parameters there are a number of
buttons on the widget for modifying the table. They are:
+: adds a new row after the last selected row (or last row if none
selected) ensuring that it contains a unique label.
-: deletes the selected row(s).
up: moves the selected row(s) up
down: moves the selected row(s) down
duplicate: duplicates the selected row(s)
Finally a list of 'default values' to be loaded into the table on
initialization is defined using ``self.default_rows``. This is passed to
``self.set_defaults(...)`` on initialization. The structure of the data to
be passed into ``self.set_defaults(...)`` and the parameters value in the
``{self._name: parameters}`` dict returned by ``get_parameters()`` has the
structure:
..code-block:: python
[{prefix1_name: prefix1_value, ..., prefixN_name: prefixN_value},
{col1_name: col1row1_value, ..., colN_name: colNrow1_value},
...,
{col1_name: col1rowN_value, ..., colN_name: colNrowN_value},
{suffix1_name: suffix1_value, ..., suffixN_name: suffixN_value}]
Parameters
----------
name : string
The name of the widget, stored on self._name
*args/**kwargs : various
args and kwargs to be passed to ``qtpy.QtWidgets.QWidget``.
prefix_editor_map : OrderedDict, optional
An OrderedDict that maps parameter names to editor widgets, for
parameters that are to be displayed above the table.
table_editor_map : OrderedDict, optional
An OrderedDict that maps column names to editor widgets, for
parameters that are to be displayed in the table.
suffix_editor_map : OrderedDict, optional
An OrderedDict that maps parameter names to editor widgets, for
parameters that are to be displayed below the table.
default_parameters : [dicts]
A list of dicts following the structure defined above that contain
default values to be loaded into the table.
title : str, optional
An optional title for the widget, used if the widget is created in its
own window.
geometry : tuple, optional
The location and size of the widget given as a tuple with the values:
``(left, top, width, height)``.
mainLayoutString : str, optional
A string that will appear above all of the widgets in the layout
"""
def __init__(self, name, *args, delegate=MTableItemDelegate,
prefix_editor_map=OrderedDict({}),
table_editor_map=OrderedDict({}),
suffix_editor_map=OrderedDict({}),
default_parameters=[],
update_coupled_parameters=None, title='Default Title',
geometry=(100, 100, 800, 300), mainLayoutString=None,
**kwargs):
super().__init__(*args, **kwargs)
self._name = name
self.prefix_editor_map = prefix_editor_map
self.table_editor_map = table_editor_map
self.suffix_editor_map = suffix_editor_map
self.default_parameters = default_parameters
self.title = title
self.geometry = geometry
self.mainLayoutString = mainLayoutString
self.setAutoFillBackground(True)
self._initUI(delegate, update_coupled_parameters)
def _initUI(self, delegate, update_coupled_parameters):
# set the title, location and size of the Widget
self.setWindowTitle(self.title)
self.setGeometry(*self.geometry)
self.mainLayout = QVBoxLayout()
# create a QLabel which describes the table
if not self.mainLayoutString:
self.mainLayoutString = ""
self.mainLabel = QLabel(self.mainLayoutString)
self.mainLayout.addWidget(self.mainLabel)
# if any global parameters are specifed in prefix_editor_map add them
if self.prefix_editor_map:
self.prefixLayout = QHBoxLayout()
for name, editor in self.prefix_editor_map.items():
setattr(self, name, editor(name, parent=self.parent()))
widget = getattr(self, name)
self.prefixLayout.addLayout(vstacked_label(name, widget))
self.mainLayout.addLayout(self.prefixLayout)
# if any table parameters are specifed in table_editor_map add them
if self.table_editor_map:
# create the table view
self.tableView = MTableInterfaceView(
self, self._name + '_view', editor_map=self.table_editor_map,
delegate=delegate,
update_coupled_parameters=update_coupled_parameters)
self.mainLayout.addWidget(self.tableView)
# enable sorting of the table
self.tableView.setSortingEnabled(True)
# if any global parameters are specifed in suffix_editor_map add them
if self.suffix_editor_map:
self.suffixLayout = QHBoxLayout()
for name, editor in self.suffix_editor_map.items():
setattr(self, name, editor(name, parent=self.parent()))
widget = getattr(self, name)
self.suffixLayout.addLayout(vstacked_label(name, widget))
self.mainLayout.addLayout(self.suffixLayout)
# load the default_entries
self.set_default(self.default_parameters)
# create and add table buttons if any table values exist
self.btnLayout = QHBoxLayout()
if self.table_editor_map:
self.addRowBtn = QPushButton('+', self)
self.addRowBtn.setToolTip('inserts a blank row(s) after the '
'selected row(s)')
self.addRowBtn.clicked.connect(self._addRow)
self.btnLayout.addWidget(self.addRowBtn)
self.delRowBtn = QPushButton('-', self)
self.delRowBtn.setToolTip('deletes the selected row(s)')
self.delRowBtn.clicked.connect(self._delRow)
self.btnLayout.addWidget(self.delRowBtn)
self.upRowBtn = QPushButton('up', self)
self.upRowBtn.setToolTip('move currently selected row down')
self.upRowBtn.clicked.connect(self._upRow)
self.btnLayout.addWidget(self.upRowBtn)
self.downRowBtn = QPushButton('down', self)
self.downRowBtn.setToolTip('move currently selected row down')
self.downRowBtn.clicked.connect(self._downRow)
self.btnLayout.addWidget(self.downRowBtn)
self.duplicateRowBtn = QPushButton('duplicate', self)
self.duplicateRowBtn.setToolTip('inserts a duplicate of the '
'selected row(s)')
self.duplicateRowBtn.clicked.connect(self._duplicateRow)
self.btnLayout.addWidget(self.duplicateRowBtn)
# create the layout and add the widgets
self.mainLayout.addLayout(self.btnLayout)
self.setLayout(self.mainLayout)
def set_default(self, parameters):
"""Sets the default values from 'parameters' to the model.
Sets the data from 'parameters' to the model, overwriting any existing
data in the model. This follows the ``mily.widget`` API.
Parameters
----------
parameters : [dicts]
List of dicts with each dict being a row that maps the column
header to its value.
"""
# if parameters is None set it to an empty list.
if not parameters:
parameters = []
else:
# extract and set prefix parameters
prefix_parameters = parameters.pop(0)
for parameter, value in prefix_parameters.items():
editor = getattr(self, parameter)
editor.set_default(value)
# extract and set suffix parameters
suffix_parameters = parameters.pop(-1)
for parameter, value in suffix_parameters.items():
editor = getattr(self, parameter)
editor.set_default(value)
# ask self.tableView to set other parameters
if self.table_editor_map:
self.tableView.set_default(parameters)
def get_parameters(self):
"""Return the entire data from the table.
Returns the entire table data as a list of dicts, with each dict being
a row that maps the column header to it's value. This follows the
``mily.widget`` API.
"""
parameters = []
# add prefix_dict
parameters.append(self.get_prefix_parameters()[self._name])
# add table dicts
if self.table_editor_map:
view_list = self.tableView.get_parameters()[self.tableView._name]
else:
view_list = {}
parameters.extend(view_list)
# add suffix dict
parameters.append(self.get_suffix_parameters()[self._name])
return {self._name: parameters}
def get_prefix_parameters(self):
"""Returns the data from the prefix widgets.
Returns a dictionary mapping the prefix parameter names to their
values.
"""
parameters = {}
for parameter in self.prefix_editor_map.keys():
editor = getattr(self, parameter)
parameters.update(editor.get_parameters())
return {self._name: parameters}
def get_suffix_parameters(self):
"""Returns the data from the suffix widgets.
Returns a dictionary mapping the suffix parameter names to their
values.
"""
parameters = {}
for parameter in self.suffix_editor_map.keys():
editor = getattr(self, parameter)
parameters.update(editor.get_parameters())
return {self._name: parameters}
def get_row_parameters(self, row):
"""Returns the data associated with the row defined by 'row'.
Returns the data associated with row as a dictionary mapping column
name to value, and any prefix or suffix data based on the value of the
kwargs prefix and suffix.
Parameters
----------
row : int
The row number who's data should be extracted.
Returns
-------
parameters : dict
A dictionary mapping kwargs to values.
"""
if self.table_editor_map:
params = self.tableView.get_row_parameters(
row)[self.tableView._name]
else:
params = {}
return {self._name: params}
def _addRow(self):
"""Inserts an empty row after the (last) currently selected row(s)."""
indices = self.tableView.selectionModel().selectedIndexes()
rows = [index.row() for index in indices]
rows.sort(reverse=True)
empty_row = []
for column in range(self.tableView.model().columnCount()):
item = QStandardItem()
item.setData(None, Qt.DisplayRole)
empty_row.append(item)
if rows: # add an empty row after the last selected row
self.tableView.model().insertRow(rows[0] + 1, empty_row)
else: # If no rows selected add row at end of table
end_row = self.tableView.model().rowCount()
self.tableView.model().insertRow(end_row, empty_row)
self._check_table_after_row_manipulation()
def _delRow(self):
"""Deletes the selected row(s)."""
indices = self.tableView.selectionModel().selectedIndexes()
rows = [index.row() for index in indices]
rows.sort(reverse=True)
if self._check_rows(rows):
for row in rows:
self.tableView.model().takeRow(row)
self._check_table_after_row_manipulation()
def _upRow(self):
"""Moves the currently selected row(s) up one."""
indices = self.tableView.selectionModel().selectedIndexes()
rows = [index.row()
for index in indices
if index.row() != 0]
rows.sort()
if self._check_rows(rows):
for row in rows:
items = self.tableView.model().takeRow(row)
self.tableView.model().insertRow(row - 1, items)
self._check_table_after_row_manipulation()
def _downRow(self):
"""Moves the currently selected row(s) down one."""
last_row = self.tableView.model().rowCount()-1
indices = self.tableView.selectionModel().selectedIndexes()
rows = [index.row()
for index in indices
if index.row() != last_row]
rows.sort(reverse=True)
if self._check_rows(rows):
for row in rows:
items = self.tableView.model().takeRow(row)
self.tableView.model().insertRow(row + 1, items)
self._check_table_after_row_manipulation()
def _duplicateRow(self):
"""Duplicates the selected row(s) into the table after the row(s)."""
# find the selected row(s)
indices = self.tableView.selectionModel().selectedIndexes()
rows = [index.row() for index in indices]
rows.sort(reverse=True)
if self._check_rows(rows):
model = self.tableView.model()
for row in rows:
row_data = []
for column in range(model.columnCount()):
value = model.item(row, column).data(Qt.DisplayRole)
item = QStandardItem()
item.setData(value, Qt.DisplayRole)
row_data.append(item)
model.insertRow(row + 1, row_data)
self._check_table_after_row_manipulation()
def _check_rows(self, rows, only_one=False):
"""Checks how many items are in ``rows`` and alerts user if not right.
Checks the number of indices in ``rows``, alerts the user with a
popup box if there are no items in ``rows``. Alternatively if the kwarg
``only_one`` is ``True`` also alerts users that too many rows are
selected. Returns ``True`` if the right number(s) of items are in
``rows`` otherwise it returns ``False``.
Parameters
----------
rows : [row indices]
A list of row indices to be checked.
only_one : Bool, optional
A boolean that indicates if more than one row is allowed, default
is ``False``.
Returns
-------
Ok : Bool
A boolean to indicate if the number of items in row is Ok.
"""
Ok = True
if not rows: # if no cell is selected
Ok = False
warning = QMessageBox()
warning.setIcon(QMessageBox.Information)
warning.setWindowTitle('Row(s) must be selected')
warning.setText('Action not performed as no row is selected')
warning.setDetailedText('This warning generally occurs '
'because no row is selected, select a row'
' and try again')
warning.setStandardButtons(QMessageBox.Ok)
warning.exec_()
elif len(rows) > 1 and only_one:
Ok = False
warning = QMessageBox()
warning.setIcon(QMessageBox.Information)
warning.setWindowTitle('More than one row is selected')
warning.setText('Action not performed as more than one row is '
'selected')
warning.setDetailedText('This warning generally occurs '
'because there are more than one row '
'selected, unselect some rows and try '
'again')
warning.setStandardButtons(QMessageBox.Ok)
warning.exec_()
return Ok
def _check_table_after_row_manipulation(self):
"""Updates coupled arguments after row manipulation.
This method runs all of the rows in the table through the method
``self.tableView.model().update_coupled_parameters`` to ensure that
the new arrangment is ok, it will update any values that are not.
"""
if (self.table_editor_map and self.tableView.model().update_coupled_parameters):
# step through each row and check it
model = self.tableView.model()
column_names = list(self.table_editor_map.keys())
for row in range(model.rowCount()):
current_parameters = self.get_row_parameters(row)[self._name]
requested_parameters = {}
new_parameters = model.update_coupled_parameters(
requested_parameters, current_parameters, row)
for column_name, value in new_parameters.items():
if value != current_parameters[column_name]:
column = column_names.index(column_name)
model.item(row, column).setData(value, Qt.DisplayRole)
class MFunctionTableInterfaceWidget(MTableInterfaceWidget):
"""Extends the MTableInterfaceWidget by adding an associated function.
Extends the MTableInterfaceWidget by associating the table with a kwarg
only function, where each kwarg for the function maps to a table column, a
prefix parameter or a suffix parameter. It also adds the extra buttons:
export: exports the selected row by calling ``self.function(...)`` with
the kwargs from the selected row and any prefix or suffix values.
Does not work with multiple rows selected.
Parameters
----------
function : func
The function associated with this table input.
*args/**kwargs : various
args and kwargs to be passed to the parent
``mily.MTableInterfaceWidget``.
"""
def __init__(self, function, *args, **kwargs):
self.function = function
super().__init__(*args, **kwargs)
self.executeBtn = QPushButton('execute', self)
self.executeBtn.setToolTip('executes the "function" with "kwargs" '
'from the selected row')
self.executeBtn.clicked.connect(self.execute)
self.btnLayout.addWidget(self.executeBtn)
def execute(self):
"""Executes the function for the selected row"""
indices = self.tableView.selectionModel().selectedIndexes()
rows = [index.row() for index in indices]
if self._check_rows(rows, only_one=True):
row = rows[0]
parameters = {}
# add the prefix parameter data (if any)
parameters.update(self.get_prefix_parameters()[self._name])
# add tableView parameters
parameters.update(self.get_row_parameters(row)[self._name])
# add the suffix parameter data (if any)
parameters.update(self.get_suffix_parameters()[self._name])
self.function(**parameters)
|
import datetime
import re
from freenit.db import db
from peewee import BooleanField, DateTimeField, ForeignKeyField, TextField
from unidecode import unidecode
from ..date import datetime_format
from .user import User
_punct_re = re.compile(r'[\t !"#$%&\'()*\-/<=>?@\[\\\]^_`{|},.]+')
Model = db.Model
class Blog(Model):
author = ForeignKeyField(User, backref='blogs')
content = TextField()
date = DateTimeField(
formats=[datetime_format],
default=datetime.datetime.utcnow
)
published = BooleanField()
slug = TextField()
title = TextField()
def save(self, *args, **kwargs):
if self.slug is None:
result = []
for word in _punct_re.split(self.title.lower()):
result.extend(unidecode(word).split())
self.slug = '-'.join(result)
super(Blog, self).save(*args, **kwargs)
@classmethod
def find(cls, year, month, day, slug):
intyear = int(year)
intmonth = int(month)
intday = int(day)
startdate_query = Blog.select().where(
Blog.date >= datetime.date(intyear,
intmonth,
intday)
)
enddate_query = startdate_query.where(
Blog.date < datetime.date(intyear,
intmonth,
intday + 1)
)
query = enddate_query.where(Blog.slug == slug)
if query.count() == 0:
raise cls.DoesNotExist
if query.count() > 1:
raise ValueError('Too many instances')
return query[0]
|
# -*- coding: utf-8 -*-
import json
import boto3
import time
from build_info import BuildInfo, CodeBuildInfo
from slack_helper import post_build_msg, find_message_for_build, send_codepipeline_result
from message_builder import MessageBuilder
codepipeline_client = boto3.client('codepipeline')
codebuild_client = boto3.client('codebuild')
def findRevisionInfo(info):
r = codepipeline_client.get_pipeline_execution(
pipelineName=info.pipeline,
pipelineExecutionId=info.executionId
)['pipelineExecution']
revs = r.get('artifactRevisions', [])
if len(revs) > 0:
return revs[0]
return None
def pipelineFromBuild(codeBuildInfo):
r = codepipeline_client.get_pipeline_state(name=codeBuildInfo.pipeline)
for s in r['stageStates']:
for a in s['actionStates']:
executionId = a.get('latestExecution', {}).get(
'externalExecutionId')
if executionId and codeBuildInfo.buildId.endswith(executionId):
pe = s['latestExecution']['pipelineExecutionId']
return (s['stageName'], pe, a)
return (None, None, None)
def processCodePipeline(event):
buildInfo = BuildInfo.fromEvent(event)
existing_msg = find_message_for_build(buildInfo)
builder = MessageBuilder(buildInfo, existing_msg)
send_reply = builder.updatePipelineEvent(event)
if builder.needsRevisionInfo():
revision = findRevisionInfo(buildInfo)
builder.attachRevisionInfo(revision)
post_build_msg(builder)
if send_reply:
send_codepipeline_result(builder)
def processCodeBuild(event):
event_id = event['detail']['build-id'].split('/')[1]
build_status = codebuild_client.batch_get_builds(ids=[event_id])
pid = event_id.split(':')[1] or None
if not pid:
return
pipeline_name = event_id.split(':')[0]
cbi = CodeBuildInfo(build_status['builds'][0]['initiator'][13:], event_id)
(stage, pid, actionStates) = pipelineFromBuild(cbi)
buildInfo = BuildInfo(pid,pipeline_name)
existing_msg = find_message_for_build(buildInfo)
builder = MessageBuilder(buildInfo, existing_msg)
phases = build_status['builds'][0]['phases']
builder.updateBuildStageInfo(stage, phases, actionStates)
logs = build_status['builds'][0].get('logs', {})
try:
if logs['streamName']:
builder.attachLogs(
logs)
except KeyError:
pass
post_build_msg(builder)
def process(event):
if event['source'] == "aws.codepipeline":
processCodePipeline(event)
if event['source'] == "aws.codebuild":
processCodeBuild(event)
def run(event, context):
# print(json.dumps(event, indent=2, default=str))
process(event)
if __name__ == "__main__":
with open('full_test.json') as f:
events = json.load(f)
for e in events:
run(e, {})
time.sleep(1)
|
from django.shortcuts import render, redirect
# Login needed decorator
from django.contrib.auth.decorators import login_required
from reports.forms import Report_Form
from reports.models import Report
from patients.models import Patient
""" Reportlab modules """
import io
from django.http import FileResponse
from reportlab.pdfgen import canvas
@login_required(login_url='/login/')
def report_creation(request):
#Get the patients list
patients = Patient.objects.filter(user=request.user,status='A')
if request.method == 'GET':
form = Report_Form()
context = {
'form':form,
'patients':patients
}
else:
# POST
form = Report_Form(request.POST)
context = {
'form':form,
'patients':patients
}
if form.is_valid():
form.save()
return redirect('home')
return render(request,'report_creation.html', context)
@login_required(login_url='/login/')
def report_update(request,id):
#Get the patients list
patients = Patient.objects.filter(user=request.user,status='A')
#Get the report list
report = Report.objects.get(id = id)
if request.method == 'GET':
form = Report_Form(instance=report)
context = {
'form':form,
'patients':patients
}
else:
# POST update instance
form = Report_Form(request.POST, instance=report)
context = {
'form':form,
'patients':patients
}
if form.is_valid():
form.save()
return redirect('home')
return render(request,'report_creation.html',context)
@login_required(login_url='/login/')
def report_delete(request,id):
report = Report.objects.get(id = id)
report.delete()
return redirect('home')
def report_pdf(request,id_number):
patient = Patient.objects.get(id_number=id_number)
# Create a file-like buffer to receive PDF data.
buffer = io.BytesIO()
# Create the PDF object, using the buffer as its "file."
p = canvas.Canvas(buffer)
# Draw things on the PDF. Here's where the PDF generation happens.
# See the ReportLab documentation for the full list of functionality.
p.drawString(100, 100, 'Hello PDF')
# Close the PDF object cleanly, and we're done.
p.showPage()
p.save()
# FileResponse sets the Content-Disposition header so that browsers
# present the option to save the file.
buffer.seek(0)
return FileResponse(buffer, as_attachment=True, filename='Reporte.pdf')
|
#%% Imports
from operator import itemgetter
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
from graspy.cluster import GaussianCluster, KMeansCluster
from graspy.embed import AdjacencySpectralEmbed, LaplacianSpectralEmbed, OmnibusEmbed
from graspy.models import DCSBMEstimator
from graspy.plot import gridplot, heatmap, pairplot
from graspy.utils import augment_diagonal, binarize, cartprod, pass_to_ranks, to_laplace
from joblib.parallel import Parallel, delayed
from mpl_toolkits.axes_grid1 import make_axes_locatable
from scipy.stats import entropy
from sklearn.cluster import KMeans
from sklearn.metrics import adjusted_rand_score
from sklearn.mixture import GaussianMixture
from sklearn.model_selection import ParameterGrid
from spherecluster import SphericalKMeans
from src.data import load_everything, load_networkx
from src.models import GridSearchUS
from src.utils import get_best, meta_to_array, relabel, savefig
from src.visualization import incidence_plot, screeplot
# Global general parameters
MB_VERSION = "mb_2019-09-23"
BRAIN_VERSION = "2019-09-18-v2"
GRAPH_TYPES = ["Gad", "Gaa", "Gdd", "Gda"]
GRAPH_TYPE_LABELS = [r"A $\to$ D", r"A $\to$ A", r"D $\to$ D", r"D $\to$ A"]
N_GRAPH_TYPES = len(GRAPH_TYPES)
SAVEFIGS = True
# Functions
def annotate_arrow(ax, coords=(0.061, 0.93)):
arrow_args = dict(
arrowstyle="-|>",
color="k",
connectionstyle="arc3,rad=-0.4", # "angle3,angleA=90,angleB=90"
)
t = ax.annotate("Target", xy=coords, xycoords="figure fraction")
ax.annotate(
"Source", xy=(0, 0.5), xycoords=t, xytext=(-1.4, -2.1), arrowprops=arrow_args
)
def ase(adj, n_components):
if PTR:
adj = pass_to_ranks(adj)
ase = AdjacencySpectralEmbed(n_components=n_components)
latent = ase.fit_transform(adj)
latent = np.concatenate(latent, axis=-1)
return latent
def omni(adjs, n_components):
if PTR:
adjs = [pass_to_ranks(a) for a in adjs]
omni = OmnibusEmbed(n_components=n_components // len(adjs))
latent = omni.fit_transform(adjs)
latent = np.concatenate(latent, axis=-1) # first is for in/out
latent = np.concatenate(latent, axis=-1) # second is for concat. each graph
return latent
def ase_concatenate(adjs, n_components):
if PTR:
adjs = [pass_to_ranks(a) for a in adjs]
ase = AdjacencySpectralEmbed(n_components=n_components // len(adjs))
graph_latents = []
for a in adjs:
latent = ase.fit_transform(a)
latent = np.concatenate(latent, axis=-1)
graph_latents.append(latent)
latent = np.concatenate(graph_latents, axis=-1)
return latent
def degree(adjs, *args):
deg_mat = np.zeros((n_verts, 2 * N_GRAPH_TYPES))
for i, g in enumerate(adjs):
deg_mat[:, i] = g.sum(axis=0)
deg_mat[:, i + N_GRAPH_TYPES] = g.sum(axis=1)
return deg_mat
def calc_weighted_entropy(true_labels, pred_labels):
total_entropy = 0
unique_true_labels = np.unique(true_labels)
unique_pred_labels = np.unique(pred_labels)
for true_label in unique_true_labels:
if (
true_label == -1 or true_label == "Unknown"
): # this is for "unlabeled" points
continue
probs = np.zeros(unique_pred_labels.shape)
true_inds = np.where(true_labels == true_label)[0]
class_pred_labels = pred_labels[
true_inds
] # get the predicted class assignments for this true class
uni_inds, counts = np.unique(class_pred_labels, return_counts=True)
probs[uni_inds] = counts
probs /= len(class_pred_labels)
e = entropy(probs)
e *= len(class_pred_labels) / len(true_labels)
e /= np.log(len(unique_pred_labels))
total_entropy += e
return total_entropy
def generate_experiment_arglist(latents, true_labels):
arglist = []
for i, (latent, latent_name) in enumerate(zip(latents, EMBED_FUNC_NAMES)):
for j, (estimator, estimator_name) in enumerate(
zip(ESTIMATORS, ESTIMATOR_NAMES)
):
for k in range(MIN_CLUSTERS, MAX_CLUSTERS):
arglist.append(
(
true_labels,
latent,
latent_name,
estimator,
estimator_name,
k,
params[j],
)
)
return arglist
def ari_scorer(estimator, latent, y=None):
pred_labels = estimator.fit_predict(latent)
return adjusted_rand_score(y, pred_labels)
def entropy_scorer(estimator, latent, y=None):
pred_labels = estimator.fit_predict(latent)
return calc_weighted_entropy(y, pred_labels)
def bic_scorer(estimator, latent, y=None):
if type(estimator) == GaussianCluster:
bic = estimator.model_.bic(latent)
return bic
else:
return np.nan
def inertia_scorer(estimator, latent, y=None):
if type(estimator) == KMeans or type(estimator) == SphericalKMeans:
inert = estimator.inertia_
return inert
else:
return np.nan
def run_clustering(
seed,
true_labels,
latent,
latent_name,
estimator,
estimator_name,
n_clusters,
params,
):
np.random.seed(seed)
if estimator == GaussianCluster:
e = estimator(min_components=n_clusters, max_components=n_clusters, **params)
else:
e = estimator(n_clusters=n_clusters, **params)
e.fit(latent)
ari = ari_scorer(e, latent, y=true_labels)
ent = entropy_scorer(e, latent, y=true_labels)
bic = bic_scorer(e, latent, y=true_labels)
inert = inertia_scorer(e, latent, y=true_labels)
out_dict = {
"ARI": ari,
"Entropy": ent,
"Embed": latent_name,
"Cluster": estimator_name,
"# Clusters": n_clusters,
"BIC": bic,
"Inertia": inert,
}
return out_dict
def run_clustering_experiment(
latents, true_labels, min_clusters, max_clusters, n_sims, seed=None
):
if seed is not None:
np.random.seed(seed)
arglist = generate_experiment_arglist(latents, true_labels)
arglist = arglist * n_sims
seeds = np.random.randint(1e8, size=n_sims * len(arglist))
outs = Parallel(n_jobs=-2, verbose=10)(
delayed(run_clustering)(s, *i) for s, i in zip(seeds, arglist)
)
cluster_df = pd.DataFrame.from_dict(outs)
return cluster_df
# Global alg parameters
PTR = True
EMBED_FUNC_NAMES = ["ASE", "OMNI", "Degree"] # "ASE-Cat"]
EMBED_FUNCS = [ase, omni, degree] # ase_concatenate]
ESTIMATORS = [GaussianCluster, SphericalKMeans, KMeans]
ESTIMATOR_NAMES = ["GMM", "SKmeans", "Kmeans"]
MAX_CLUSTERS = 12
MIN_CLUSTERS = 2
N_SIMS = 1
N_INIT = 200
# Set up plotting constants
plt.style.use("seaborn-white")
sns.set_palette("deep")
sns.set_context("talk", font_scale=1)
# Experiment 1: Compare clustering on right mushroom body
# Preliminaries:
# Load the right mushroom body data
# Plot the summed graph
# Plot the 4-color graphs, split up
# Plot the ASE on summed latent positions
# Plot the OMNI on 4-color latent positions
# Plot the MASE on 4-color latent positions
# Plot the split 4-color ASE concatenated positions
# TODO: Compare to LSE
# Experiment:
# Cluster each of the above embeddings using skmeans, kmeans, gmm
# Plot ARI vs. number of clusters
# Plot Entropy metric vs. number of clusters
#%% Load the Mushroom Body Right
# Load graph and some metadata
adj, class_labels, side_labels = load_everything(
"G", version=MB_VERSION, return_class=True, return_side=True
)
right_inds = np.where(side_labels == "right")[0]
adj = adj[np.ix_(right_inds, right_inds)]
degrees = adj.sum(axis=0) + adj.sum(axis=1)
sort_inds = np.argsort(degrees)[::-1]
class_labels = class_labels[right_inds] # need to do right inds, then sort_inds
class_labels = class_labels[sort_inds]
# Remap the names
name_map = {
"APL": "APL",
"Gustatory PN": "PN",
"KC 1 claw": "KC",
"KC 2 claw": "KC",
"KC 3 claw": "KC",
"KC 4 claw": "KC",
"KC 5 claw": "KC",
"KC 6 claw": "KC",
"KC young": "KC",
"MBIN": "MBIN",
"MBON": "MBON",
"ORN mPN": "PN",
"ORN uPN": "PN",
"Unknown PN": "PN",
"tPN": "PN",
"vPN": "PN",
}
simple_class_labels = np.array(itemgetter(*class_labels)(name_map))
# Now load all 4 colors
color_adjs = []
for t in GRAPH_TYPES:
adj = load_everything(t, version=MB_VERSION)
adj = adj[np.ix_(right_inds, right_inds)]
adj = adj[np.ix_(sort_inds, sort_inds)]
color_adjs.append(adj)
sum_adj = np.array(color_adjs).sum(axis=0)
# Print some stats
n_verts = adj.shape[0]
print("Right Mushroom Body")
print()
print(f"Number of vertices: {n_verts}")
print()
for g, name in zip(color_adjs, GRAPH_TYPES):
print(name)
print(f"Number of edges: {np.count_nonzero(g)}")
print(f"Number of synapses: {int(g.sum())}")
median_in_degree = np.median(np.count_nonzero(g, axis=0))
median_out_degree = np.median(np.count_nonzero(g, axis=1))
print(f"Median node in degree: {median_in_degree}")
print(f"Median node out degree: {median_out_degree}")
print()
#%%
# Plot the adjacency matrix for the summed graph
plt.figure(figsize=(5, 5))
ax = heatmap(
sum_adj,
inner_hier_labels=simple_class_labels,
transform="simple-all",
hier_label_fontsize=18,
sort_nodes=False,
cbar=False,
title="Right Mushroom Body (summed 4 channels)",
title_pad=90,
font_scale=1.7,
)
annotate_arrow(ax, (0.135, 0.88))
savefig("flat_mb", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
# Plot the adjacency matrix for the 4-color graphs
fig, ax = plt.subplots(2, 2, figsize=(20, 20))
ax = ax.ravel()
for i, g in enumerate(color_adjs):
heatmap(
g,
inner_hier_labels=simple_class_labels,
transform="simple-all",
hier_label_fontsize=18,
sort_nodes=False,
ax=ax[i],
cbar=False,
title=GRAPH_TYPE_LABELS[i],
title_pad=70,
font_scale=1.7,
)
plt.suptitle("Right Mushroom Body (4 channels)", fontsize=45, x=0.525, y=1.02)
plt.tight_layout()
annotate_arrow(ax[0])
savefig("4color_mb", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
#%% Embed the graphs for the mushroom body right
n_components = 4
ase_latent = ase(sum_adj, n_components)
omni_latent = omni(color_adjs, n_components)
ase_cat_latent = ase_concatenate(color_adjs, n_components)
degree_mat = degree(color_adjs)
# latents = [ase_latent, omni_latent, ase_cat_latent, degree_mat]
latents = [ase_latent, omni_latent, degree_mat]
for latent, name in zip(latents, EMBED_FUNC_NAMES):
pairplot(latent, labels=simple_class_labels, title=name)
#%%
# degree_clusts = [SphericalKMeans, KMeans]
# for k in range(2, 12):
# print(k)
# est = SphericalKMeans(n_clusters=k)
# pred_labels = est.fit_predict(deg_mat)
# ari = adjusted_rand_score(simple_class_labels, pred_labels)
# print(ari)
# print()
# for k in range(2, 12):
# print(k)
# est = KMeans(n_clusters=k)
# pred_labels = est.fit_predict(deg_mat)
# ari = adjusted_rand_score(simple_class_labels, pred_labels)
# print(ari)
# for k in range(2, 12):
# print(k)
# est = GaussianCluster(min_components=k, max_components=k, covariance_type="all")
# pred_labels = est.fit_predict(deg_mat)
# ari = adjusted_rand_score(simple_class_labels, pred_labels)
# print(ari)
#%% Run a clustering experiment on the mushroom body right
gmm_params = {"n_init": N_INIT, "covariance_type": "all"}
skmeans_params = {"n_init": N_INIT}
kmeans_params = {"n_init": N_INIT}
true_labels = simple_class_labels
params = [gmm_params, skmeans_params, kmeans_params]
cluster_df = run_clustering_experiment(
latents, true_labels, MIN_CLUSTERS, MAX_CLUSTERS, N_SIMS, seed=8888
)
#%% Plot results of clustering experiments
sns.set_context("talk", font_scale=1.75)
figsize = (20, 10)
plt.figure(figsize=figsize)
sns.lineplot(
data=cluster_df,
x="# Clusters",
y="ARI",
hue="Embed",
hue_order=EMBED_FUNC_NAMES,
style="Cluster",
style_order=ESTIMATOR_NAMES,
)
plt.legend(bbox_to_anchor=(1, 1))
plt.title(f"Right MB, n_inits = {N_INIT}")
savefig("right_mb_ari", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
plt.figure(figsize=figsize)
sns.lineplot(
data=cluster_df,
x="# Clusters",
y="Entropy",
hue="Embed",
hue_order=EMBED_FUNC_NAMES,
style="Cluster",
style_order=ESTIMATOR_NAMES,
)
plt.legend(bbox_to_anchor=(1, 1))
plt.title(f"Right MB, n_inits = {N_INIT}")
savefig("right_mb_ent", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
plot_bic_df = cluster_df.sort_values("BIC", ascending=False).drop_duplicates(
["Embed", "Cluster", "# Clusters"]
)
plt.figure(figsize=figsize)
sns.lineplot(
data=plot_bic_df,
x="# Clusters",
y="BIC",
hue="Embed",
hue_order=EMBED_FUNC_NAMES,
style="Cluster",
style_order=ESTIMATOR_NAMES,
)
plt.legend(bbox_to_anchor=(1, 1))
plt.title(f"Right MB, n_inits = {N_INIT}")
savefig("right_mb_bic", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
#%%
adj, class_labels, side_labels = load_everything(
"G", version=BRAIN_VERSION, return_class=True, return_side=True
)
right_inds = np.where(side_labels == " mw right")[0]
adj = adj[np.ix_(right_inds, right_inds)]
degrees = adj.sum(axis=0) + adj.sum(axis=1)
sort_inds = np.argsort(degrees)[::-1]
class_labels = class_labels[right_inds] # need to do right inds, then sort_inds
class_labels = class_labels[sort_inds]
# Remap the names
name_map = {
"CN": "Unknown",
"DANs": "MBIN",
"KCs": "KC",
"LHN": "Unknown",
"LHN; CN": "Unknown",
"MBINs": "MBIN",
"MBON": "MBON",
"MBON; CN": "MBON",
"OANs": "MBIN",
"ORN mPNs": "PN",
"ORN uPNs": "PN",
"tPNs": "PN",
"vPNs": "PN",
"Unidentified": "Unknown",
"Other": "Unknown",
}
simple_class_labels = np.array(itemgetter(*class_labels)(name_map))
# Now load all 4 colors
color_adjs = []
for t in GRAPH_TYPES:
adj = load_everything(t)
adj = adj[np.ix_(right_inds, right_inds)]
adj = adj[np.ix_(sort_inds, sort_inds)]
color_adjs.append(adj)
sum_adj = np.array(color_adjs).sum(axis=0)
# Print some stats
n_verts = adj.shape[0]
print("Right Brain")
print()
print(f"Number of vertices: {n_verts}")
print()
for g, name in zip(color_adjs, GRAPH_TYPES):
print(name)
print(f"Number of edges: {np.count_nonzero(g)}")
print(f"Number of synapses: {int(g.sum())}")
median_in_degree = np.median(np.count_nonzero(g, axis=0))
median_out_degree = np.median(np.count_nonzero(g, axis=1))
print(f"Median node in degree: {median_in_degree}")
print(f"Median node out degree: {median_out_degree}")
print()
# Plot the adjacency matrix for the summed graph
sns.set_context("talk", font_scale=1)
plt.figure(figsize=(5, 5))
ax = heatmap(
sum_adj,
inner_hier_labels=simple_class_labels,
transform="simple-all",
hier_label_fontsize=10,
sort_nodes=False,
cbar=False,
title="Right Brain (summed 4 channels)",
title_pad=90,
font_scale=1.7,
)
annotate_arrow(ax, (0.135, 0.88))
# Plot the adjacency matrix for the 4-color graphs
fig, ax = plt.subplots(2, 2, figsize=(20, 20))
ax = ax.ravel()
for i, g in enumerate(color_adjs):
heatmap(
binarize(g),
inner_hier_labels=simple_class_labels,
# transform="si",
hier_label_fontsize=10,
sort_nodes=False,
ax=ax[i],
cbar=False,
title=GRAPH_TYPE_LABELS[i],
title_pad=70,
font_scale=1.7,
)
plt.suptitle("Right Brain (4 channels)", fontsize=45, x=0.525, y=1.02)
plt.tight_layout()
annotate_arrow(ax[0])
savefig("4color_brain", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
#%% Embed the graphs for the right hemisphere graph
n_components = 4
ase_latent = ase(sum_adj, n_components)
omni_latent = omni(color_adjs, n_components)
ase_cat_latent = ase_concatenate(color_adjs, n_components)
latents = [ase_latent, omni_latent, ase_cat_latent]
for latent, name in zip(latents, EMBED_FUNC_NAMES):
pairplot(latent, labels=simple_class_labels, title=name)
#%% Run a clustering experiment on the full graph right
gmm_params = {"n_init": N_INIT, "covariance_type": "all"}
skmeans_params = {"n_init": N_INIT}
kmeans_params = {"n_init": N_INIT}
true_labels = simple_class_labels
params = [gmm_params, skmeans_params, kmeans_params]
cluster_df = run_clustering_experiment(
latents, true_labels, MIN_CLUSTERS, MAX_CLUSTERS, N_SIMS, seed=8888
)
#%% Plot results of clustering experiments
sns.set_context("talk", font_scale=1.75)
figsize = (20, 10)
plt.figure(figsize=figsize)
sns.lineplot(
data=cluster_df,
x="# Clusters",
y="Entropy",
hue="Embed",
hue_order=EMBED_FUNC_NAMES,
style="Cluster",
style_order=ESTIMATOR_NAMES,
)
plt.legend(bbox_to_anchor=(1, 1))
plt.title(f"Entropy, n_init = {N_INIT}")
savefig("right_brain_ent", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
plot_ari_df = cluster_df.sort_values("BIC", ascending=False).drop_duplicates(
["Embed", "Cluster", "# Clusters"]
)
plt.figure(figsize=figsize)
sns.lineplot(
data=plot_ari_df,
x="# Clusters",
y="BIC",
hue="Embed",
hue_order=EMBED_FUNC_NAMES,
style="Cluster",
style_order=ESTIMATOR_NAMES,
)
plt.legend(bbox_to_anchor=(1, 1))
plt.title(f"BIC, n_init = {N_INIT}")
savefig("right_brain_bic", fmt="png", dpi=150, bbox_inches="tight", pad_inches=0.5)
#####################
# Experiment 2: Compare clustering on the full mushroom body
# Preliminaries:
# Load the full mushroom body
# Generate same visualization plots as for the above
# Experiment:
# Same plots as for Experiment 1
# Other
# Get best ARI
# plot_ari_df = cluster_df.sort_values("ARI", ascending=False).drop_duplicates(
# ["Embed", "Cluster", "# Clusters"]
# )
# plt.figure(figsize=figsize)
# sns.lineplot(data=cluster_df, x="# Clusters", y="ARI", hue="Embed", style="Cluster")
# plt.legend(bbox_to_anchor=(1, 1))
# plt.title(f"Mean ARIs +/- 95% CI, n_sims = {n_sims}")
# Get best entropy
# plot_ent_df = cluster_df.sort_values("Entropy", ascending=True).drop_duplicates(
# ["Embed", "Cluster", "# Clusters"]
# )
# plt.figure(figsize=figsize)
# sns.lineplot(data=cluster_df, x="# Clusters", y="Entropy", hue="Embed",
# style="Cluster")
# plt.legend(bbox_to_anchor=(1, 1))
# plt.title(f"Mean entropy +/- 95% CI, n_sims = {n_sims}")
# Experiment 3: Compare clustering on one hemisphere of the full data
# Preliminaries:
# Load the full graph
# Generate the same visualization plots as for the above
# Experiment:
# Same plots as for Experiment 1
# %%
|
# Copyright (c) 2020-2021, Cenobit Technologies, Inc. http://cenobit.es/
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
# * Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
# * Neither the name of the Cenobit Technologies nor the names of
# its contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
import sys
import traceback
from typing import Any, Dict, Optional
from flask import current_app
try:
from flaskext.babel import gettext as _ # type: ignore
_("You're lazy...") # this function lazy-loads settings (pragma: no cover)
except (ImportError, NameError):
_ = lambda t, *a, **k: t # noqa: E731
class JSONRPCError(Exception):
"""Error class based on the JSON-RPC 2.0 specs
https://www.jsonrpc.org/specification
message - string
code - number
data - object
status_code - number from https://www.jsonrpc.org/specification_v1#a2.2JSON-RPCoverHTTP
JSON-RPC over HTTP Errors section
"""
code: int = 0
message: Optional[str] = None
data: Optional[Any] = None
status_code: int = 400
def __init__(
self,
message: Optional[str] = None,
code: Optional[int] = None,
data: Optional[Any] = None,
status_code: Optional[int] = None,
) -> None:
"""Setup the Exception and overwrite the default message"""
super().__init__()
if message is not None:
self.message = message
if code is not None:
self.code = code
if data is not None:
self.data = data
if status_code is not None:
self.status_code = status_code
@property
def jsonrpc_format(self) -> Dict[str, Any]:
"""Return the Exception data in a format for JSON-RPC"""
error = {
'name': self.__class__.__name__,
'code': self.code,
'message': self.message,
'data': self.data,
}
# RuntimeError: Working outside of application context.
# This typically means that you attempted to use functionality that needed
# to interface with the current application object in some way. To solve
# this, set up an application context with app.app_context(). See the
# documentation for more information.
if current_app and current_app.config['DEBUG']: # pragma: no cover
error['stack'] = traceback.format_exc()
error['executable'] = sys.executable
return error
# The error codes from and including -32768 to -32000 are reserved for
# pre-defined errors. Any code within this range, but not defined explicitly
# below is reserved for future use. The error codes are nearly the same as
# those suggested for XML-RPC at the following url:
# http://xmlrpc-epi.sourceforge.net/specs/rfc.fault_codes.php
class ParseError(JSONRPCError):
"""Invalid JSON was received by the server.
An error occurred on the server while parsing the JSON text.
"""
code = -32700
message = _('Parse error')
class InvalidRequestError(JSONRPCError):
"""The JSON sent is not a valid Request object."""
code = -32600
message = _('Invalid Request')
class MethodNotFoundError(JSONRPCError):
"""The method does not exist / is not available."""
code = -32601
message = _('Method not found')
class InvalidParamsError(JSONRPCError):
"""Invalid method parameter(s)."""
code = -32602
message = _('Invalid params')
class InternalError(JSONRPCError):
"""Internal JSON-RPC error."""
code = -32603
message = _('Internal error')
class ServerError(JSONRPCError):
"""Reserved for implementation-defined server-errors.
code: -32000 to -32099 Server error.
"""
code = -32000
message = _('Server error')
status_code = 500
|
import snitch
from snitch import explicit_dispatch
from snitch.constants import DEFAULT_CONFIG
from tests.app.events import DUMMY_EVENT
@snitch.dispatch(DUMMY_EVENT, config=DEFAULT_CONFIG)
def dispatch_dummy_event(actor, trigger, target):
pass
def dispatch_explicit_dummy_event(actor, trigger, target):
explicit_dispatch(verb=DUMMY_EVENT, actor=actor, trigger=trigger, target=target)
|
from django.test import TestCase
class LocaleTest(TestCase):
def test_set_locale_cookie(self):
response = self.client.get('/control/login')
assert response['Content-Language'] == 'en'
self.client.get('/locale/set?locale=de')
response = self.client.get('/control/login')
assert response['Content-Language'] == 'de'
|
from .tools import load_yaml, get, strict_str, KnittyError # noqa
|
from __future__ import print_function, division, absolute_import
import argparse
import os
import cv2
from tqdm import tqdm
from rt_gene.extract_landmarks_method_base import LandmarkMethodBase
script_path = os.path.dirname(os.path.realpath(__file__))
if __name__ == "__main__":
parser = argparse.ArgumentParser(description='Estimate gaze from images')
parser.add_argument('im_path', type=str, default=os.path.join(script_path, '../samples/natural'),
nargs='?', help='Path to an image or a directory containing images')
parser.add_argument('--output_path', type=str, default=os.path.join(script_path, '../samples/'), help='Output directory for left/right eye patches')
landmark_estimator = LandmarkMethodBase(device_id_facedetection="cuda:0",
checkpoint_path_face=os.path.join(script_path, "../../rt_gene/model_nets/SFD/s3fd_facedetector.pth"),
checkpoint_path_landmark=os.path.join(script_path, "../../rt_gene/model_nets/phase1_wpdc_vdc.pth.tar"),
model_points_file=os.path.join(script_path, "../../rt_gene/model_nets/face_model_68.txt"))
args = parser.parse_args()
image_path_list = []
if os.path.isfile(args.im_path):
image_path_list.append(os.path.split(args.im_path)[1])
args.im_path = os.path.split(args.im_path)[0]
elif os.path.isdir(args.im_path):
for image_file_name in os.listdir(args.im_path):
if image_file_name.endswith('.jpg') or image_file_name.endswith('.png'):
if '_gaze' not in image_file_name and '_headpose' not in image_file_name:
image_path_list.append(image_file_name)
left_folder_path = os.path.join(args.output_path, "left_new")
right_folder_path = os.path.join(args.output_path, "right_new")
if not os.path.isdir(left_folder_path):
os.makedirs(left_folder_path)
if not os.path.isdir(right_folder_path):
os.makedirs(right_folder_path)
p_bar = tqdm(image_path_list)
for image_file_name in p_bar:
p_bar.set_description("Processing {}".format(image_file_name))
image = cv2.imread(os.path.join(args.im_path, image_file_name))
if image is None:
continue
faceboxes = landmark_estimator.get_face_bb(image)
if len(faceboxes) == 0:
continue
subjects = landmark_estimator.get_subjects_from_faceboxes(image, faceboxes)
for subject in subjects:
le_c, re_c, _, _ = subject.get_eye_image_from_landmarks(subject, landmark_estimator.eye_image_size)
if le_c is not None and re_c is not None:
img_name = image_file_name.split(".")[0]
left_image_path = ["left", img_name, "rgb.png"]
left_image_path = os.path.join(left_folder_path, "_".join(left_image_path))
right_image_path = ["right", img_name, "rgb.png"]
right_image_path = os.path.join(right_folder_path, "_".join(right_image_path))
cv2.imwrite(left_image_path, le_c)
cv2.imwrite(right_image_path, re_c)
|
from django.contrib.auth.models import User
from django.template.response import TemplateResponse
from django.test import TestCase
try:
from django.urls import reverse
except ImportError:
from django.core.urlresolvers import reverse
class TopLevelAdminTestCase(TestCase):
@classmethod
def setUpTestData(cls):
cls.superuser = User.objects.create_superuser(username='super', password='secret', email='super@example.com')
def setUp(self):
try:
self.client.force_login(self.superuser)
except AttributeError:
self.client.login(username=self.superuser.username, password='secret')
def test_changelist(self):
response = self.client.get(reverse('admin:app_toplevel_changelist'))
self.assertIsInstance(response, TemplateResponse)
self.assertEqual(response.status_code, 200)
def test_add_view(self):
response = self.client.get(reverse('admin:app_toplevel_add'))
self.assertIsInstance(response, TemplateResponse)
self.assertEqual(response.status_code, 200)
|
#!/usr/bin/env python
#
# Licensed under the Apache License, Version 2.0 (the "License");
# You may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0OA
#
# Authors:
# - Wen Guan, <wen.guan@cern.ch>, 2020
"""
core operations related to workflow model.
"""
# from idds.common import exceptions
from idds.common.constants import WorkprogressStatus, WorkprogressLocking
from idds.orm.base.session import read_session, transactional_session
from idds.orm import workprogress as orm_workprogress, transforms as orm_transforms
from idds.workflow.work import WorkStatus
def create_workprogress(request_id, scope, name, priority=0, status=WorkprogressStatus.New, locking=WorkprogressLocking.Idle,
expired_at=None, errors=None, workprogress_metadata=None, processing_metadata=None):
"""
Create a workprogress.
:param request_id: The request id.
:param scope: The scope.
:param name: The name.
:param status: The status as integer.
:param locking: The locking as integer.
:param priority: The priority as integer.
:param expired_at: The datetime when the workprogress will be expired at.
:param errors: The errors as a json.
:param workprogress_metadata: The metadata as json.
:param processing_metadata: The metadata as json.
:returns: workprogress.
"""
return orm_workprogress.create_workprogress(request_id=request_id, scope=scope, name=name, priority=priority, status=status,
locking=locking, expired_at=expired_at,
workprogress_metadata=workprogress_metadata,
processing_metadata=processing_metadata)
@transactional_session
def add_workprogress(request_id, scope, name, priority=0, status=WorkprogressStatus.New, locking=WorkprogressLocking.Idle,
expired_at=None, errors=None, workprogress_metadata=None, processing_metadata=None,
session=None):
"""
Add a workprogress.
:param request_id: The request id.
:param scope: The scope.
:param name: The name.
:param status: The status as integer.
:param locking: The locking as integer.
:param priority: The priority as integer.
:param expired_at: The datetime when the workprogress will be expired at.
:param errors: The errors as a json.
:param workprogress_metadata: The metadata as json.
:param processing_metadata: The metadata as json.
:raises DuplicatedObject: If a workprogress with the same name exists.
:raises DatabaseException: If there is a database error.
:returns: workprogress id.
"""
return orm_workprogress.add_workprogress(request_id=request_id, scope=scope, name=name, priority=priority, status=status,
locking=locking, expired_at=expired_at,
workprogress_metadata=workprogress_metadata,
processing_metadata=processing_metadata,
session=session)
@transactional_session
def add_workprogresses(workprogresses, bulk_size=1000, session=None):
"""
Add workprogresses.
:param workprogresses: dict of workprogress.
:param session: session.
:raises DuplicatedObject: If a collection with the same name exists.
:raises DatabaseException: If there is a database error.
:returns: workprogress ids.
"""
return orm_workprogress.add_workprogresses(workprogresses, bulk_size=bulk_size, session=session)
@read_session
def get_workprogresses(request_id, to_json=False, session=None):
"""
Get workprogresses with request_id.
:param request_id: The request_id of the request.
:param to_json: Whether to return json format.
:param session: The database session in use.
:raises NoObject: If no workprogress is founded.
:returns: list of workprogresses.
"""
return orm_workprogress.get_workprogresses(request_id=request_id, to_json=to_json, session=session)
@read_session
def get_workprogress(workprogress_id, to_json=False, session=None):
"""
Get a workprogress or raise a NoObject exception.
:param workprogress_id: The id of the workprogress.
:param to_json: whether to return json format.
:param session: The database session in use.
:raises NoObject: If no workprogress is founded.
:returns: Workprogress.
"""
return orm_workprogress.get_workprogress(workprogress_id=workprogress_id, to_json=to_json, session=session)
@read_session
def get_workprogresses_by_status(status, period=None, locking=False, bulk_size=None, to_json=False, session=None):
"""
Get workprogresses.
:param status: list of status of the workprogress data.
:param locking: Wheter to lock workprogresses to avoid others get the same workprogress.
:param bulk_size: Size limitation per retrieve.
:param to_json: whether to return json format.
:raises NoObject: If no workprogresses are founded.
:returns: list of Workprogress.
"""
return orm_workprogress.get_workprogresses_by_status(status=status, period=period, locking=locking,
bulk_size=bulk_size, to_json=to_json, session=session)
@transactional_session
def update_workprogress(workprogress_id, parameters, new_transforms=None, session=None):
"""
update a workprogress.
:param workprogress_id: the workprogress id.
:param parameters: A dictionary of parameters.
:param session: The database session in use.
:raises NoObject: If no workprogress is founded.
:raises DatabaseException: If there is a database error.
"""
if new_transforms:
for tf in new_transforms:
tf_id = orm_transforms.add_transform(**tf, session=session)
work = tf['transform_metadata']['work']
work.set_work_id(tf_id, transforming=True)
work.set_status(WorkStatus.New)
return orm_workprogress.update_workprogress(workprogress_id=workprogress_id, parameters=parameters, session=session)
@transactional_session
def delete_workprogress(workprogress_id=None, session=None):
"""
delete a workprogress.
:param workprogress_id: The id of the workprogress.
:param session: The database session in use.
:raises NoObject: If no workprogress is founded.
:raises DatabaseException: If there is a database error.
"""
return orm_workprogress.update_workprogress(workprogress_id=workprogress_id, session=session)
@transactional_session
def clean_locking(time_period=3600, session=None):
"""
Clean locking which is older than time period.
:param time_period in seconds
"""
return orm_workprogress.clean_locking(time_period=time_period, session=session)
@transactional_session
def clean_next_poll_at(status, session=None):
"""
Clean next_poll_at.
:param status: status of the workprogress
"""
return orm_workprogress.clean_next_poll_at(status=status, session=session)
|
# ---------------------------------------------------------------------------
# |
# | FileSystem.py
# |
# | David Brownell (db@DavidBrownell.com)
# |
# | 09/05/2015 08:47:49 PM
# |
# ---------------------------------------------------------------------------
# |
# | Copyright David Brownell 2015-18.
# |
# | Distributed under the Boost Software License, Version 1.0.
# | (See accompanying file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
# |
# ---------------------------------------------------------------------------
import itertools
import os
import platform
import shutil
import stat
import sys
import time
# ---------------------------------------------------------------------------
_script_fullpath = os.path.abspath(__file__) if "python" in sys.executable.lower() else sys.executable
_script_dir, _script_name = os.path.split(_script_fullpath)
# ---------------------------------------------------------------------------
CODE_EXCLUDE_DIR_NAMES = [ "Generated",
"__pycache__",
".hg", # Mercurial
".git", # Git
".svn", # Subversion
"$tf", # Team Foundation
]
CODE_EXCLUDE_FILE_EXTENSIONS = [ # Python
".pyc",
".pyo",
]
# ----------------------------------------------------------------------
if platform.uname()[0] == "Windows":
import win32api
_is_case_sensitive_file_system = False
else:
_is_case_sensitive_file_system = True
# ---------------------------------------------------------------------------
def WalkDirs( root,
include_dir_names=None, # ex. "ASingleDir"
exclude_dir_names=None, # ex. "ASingleDir"
include_dir_paths=None, # ex. "C:\Foo\Bar"
exclude_dir_paths=None, # ex. "C:\Foo\Bar"
traverse_include_dir_names=None, # ex. "ASingleDir"
traverse_exclude_dir_names=None, # ex. "ASingleDir"
traverse_include_dir_paths=None, # ex. "C:\Foo\Bar"
traverse_exclude_dir_paths=None, # ex. "C:\Foo\Bar"
recurse=True,
include_generated=False,
):
process_dir_name = _ProcessWalkArgs(include_dir_names, exclude_dir_names)
process_dir_path = _ProcessWalkArgs(include_dir_paths, exclude_dir_paths)
process_traverse_dir_name = _ProcessWalkArgs(traverse_include_dir_names, traverse_exclude_dir_names)
process_traverse_dir_path = _ProcessWalkArgs(traverse_include_dir_paths, traverse_exclude_dir_paths)
if include_generated:
# ----------------------------------------------------------------------
def IsValid(fullpath, dir):
return ( process_traverse_dir_path(fullpath) and
process_traverse_dir_name(dir)
)
# ----------------------------------------------------------------------
else:
# ----------------------------------------------------------------------
def IsValid(fullpath, dir):
return ( dir not in CODE_EXCLUDE_DIR_NAMES and
process_traverse_dir_path(fullpath) and
process_traverse_dir_name(dir)
)
# ----------------------------------------------------------------------
from CommonEnvironment.CallOnExit import CallOnExit
root = Normalize(root)
for root, dirs, filenames in os.walk(root):
try:
root = str(root)
except UnicodeEncodeError:
continue
root = os.path.realpath(root)
# Ensure that the drive letter is uppercase
drive, path = os.path.splitdrive(root)
drive = drive.upper()
root = "{}{}".format(drive, path)
if process_dir_path(root) and process_dir_name(os.path.split(root)[1]):
yield root, filenames
index = 0
while index < len(dirs):
fullpath = os.path.join(root, dirs[index])
if not IsValid(fullpath, dirs[index]):
dirs.pop(index)
else:
index += 1
if not recurse:
dirs[:] = []
# ---------------------------------------------------------------------------
def WalkFiles( root,
include_dir_names=None, # ex. "ASingleDir"
exclude_dir_names=None, # ex. "ASingleDir"
include_dir_paths=None, # ex. "c:\foo\bar"
exclude_dir_paths=None, # ex. "c:\foo\bar"
traverse_include_dir_names=None, # ex. "ASingleDir"
traverse_exclude_dir_names=None, # ex. "ASingleDir"
traverse_include_dir_paths=None, # ex. "C:\foo\bar"
traverse_exclude_dir_paths=None, # ex. "C:\foo\bar"
include_file_base_names=None, # ex. "File" where filename is "File.ext"
exclude_file_base_names=None, # ex. "File" where filename is "File.ext"
include_file_extensions=None, # ex. ".py"
exclude_file_extensions=None, # ex. ".py"
include_file_names=None, # ex. "File.ext"
exclude_file_names=None, # ex. "File.ext"
include_full_paths=None, # ex. "C:\foo\bar\file.ext"
exclude_full_paths=None, # ex. "C:\foo\bar\file.ext"
recurse=True,
include_generated=False,
):
process_file_name = _ProcessWalkArgs(include_file_names, exclude_file_names)
process_file_base_name = _ProcessWalkArgs(include_file_base_names, exclude_file_base_names)
process_file_extension = _ProcessWalkArgs(include_file_extensions, exclude_file_extensions)
process_full_path = _ProcessWalkArgs(include_full_paths, exclude_full_paths)
for root, filenames in WalkDirs( root,
include_dir_names=include_dir_names,
exclude_dir_names=exclude_dir_names,
include_dir_paths=include_dir_paths,
exclude_dir_paths=exclude_dir_paths,
traverse_include_dir_names=traverse_include_dir_names,
traverse_exclude_dir_names=traverse_exclude_dir_names,
traverse_include_dir_paths=traverse_include_dir_paths,
traverse_exclude_dir_paths=traverse_exclude_dir_paths,
recurse=recurse,
include_generated=include_generated,
):
for filename in filenames:
if not process_file_name(filename):
continue
base_name, ext = os.path.splitext(filename)
if ( not process_file_extension(ext) or
not process_file_base_name(base_name)
):
continue
fullpath = os.path.join(root, filename)
if not process_full_path(fullpath):
continue
yield fullpath
# ----------------------------------------------------------------------
def EnumSubdirs( root,
names=False,
fullpaths=True,
):
assert os.path.isdir(root), root
if names and fullpaths:
Decorator = lambda name, fullpath: (name, fullpath)
elif names:
Decorator = lambda name, fullpath: name
elif fullpaths:
Decorator = lambda name, fullpath: fullpath
else:
assert False
for name in os.listdir(root):
fullpath = os.path.join(root, name)
if not os.path.isdir(fullpath):
continue
yield Decorator(name, fullpath)
# ---------------------------------------------------------------------------
def GetCommonPath(*items):
if not items:
return ''
if not _is_case_sensitive_file_system:
# ----------------------------------------------------------------------
def Equal(a, b):
return a.lower() == b.lower()
# ----------------------------------------------------------------------
else:
# ----------------------------------------------------------------------
def Equal(a, b):
return a == b
# ----------------------------------------------------------------------
if len(items) == 1:
result = items[0]
if os.path.isfile(result):
result = os.path.dirname(result)
return AddTrailingSep(result)
# Break the items into parts, as comparing by string leads to strange corner cases
# with similarly named paths.
items = [ os.path.realpath(item).split(os.path.sep) for item in items ]
path_index = 0
while True:
should_continue = True
for item_index, item in enumerate(items):
if path_index >= len(item):
should_continue = False
break
if item_index != 0 and not Equal(items[item_index][path_index], items[item_index - 1][path_index]):
should_continue = False
break
if not should_continue:
break
path_index += 1
if path_index == 0:
return ''
return AddTrailingSep(os.path.sep.join(items[0][:path_index]))
# ---------------------------------------------------------------------------
def GetRelativePath(source, dest):
assert source
assert dest
if os.path.isfile(source):
source = os.path.dirname(source)
source = RemoveTrailingSep(source)
dest = RemoveTrailingSep(dest)
common_prefix = GetCommonPath(source, dest)
if not common_prefix:
return dest
dest = dest[len(common_prefix):]
if dest.startswith(os.path.sep):
dest = dest[len(os.path.sep):]
source = source[len(common_prefix):]
seps = 0
for part in os.path.splitdrive(source)[1].split(os.path.sep):
if part: seps += 1
if not seps:
if not dest:
return '.'
return os.path.join(".", dest)
return "{}{}".format((("..{}".format(os.path.sep)) * seps), dest)
# ---------------------------------------------------------------------------
def RemoveTrailingSep(path):
if path == None:
return None
if path.endswith(os.path.sep):
path = path[:-len(os.path.sep)]
return path
# ----------------------------------------------------------------------
def AddTrailingSep(path):
if not path.endswith(os.path.sep):
path += os.path.sep
return path
# ----------------------------------------------------------------------
def RemoveInitialSep(path):
if path.startswith(os.path.sep):
path = path[len(os.path.sep):]
return path
# ---------------------------------------------------------------------------
def Normalize(path):
path = os.path.normpath(path)
if not _is_case_sensitive_file_system:
if os.path.exists(path):
path = win32api.GetLongPathName(win32api.GetShortPathName(path)) # <Class '<name>' has no '<attr>' member> pylint: disable = E1101
drive, suffix = os.path.splitdrive(path)
path = "{}{}".format(drive.upper(), suffix)
return path
# ----------------------------------------------------------------------
def GetSizeDisplay(num_bytes, suffix='B'):
for unit in [ '', 'K', 'M', 'G', 'T', 'P', 'E', 'Z', ]:
if num_bytes < 1024.0:
return "%3.1f %s%s" % (num_bytes, unit, suffix)
num_bytes /= 1024.0
return "%.1f %s%s" % (num_bytes, 'Yi', suffix)
# ----------------------------------------------------------------------
def CopyTree( source,
dest,
excludes=None,
output_stream=None,
):
import tqdm
from CommonEnvironment import Any, ModifiableValue
from CommonEnvironment import RegularExpression
from CommonEnvironment.StreamDecorator import StreamDecorator
regexes = []
for exclude in (excludes or []):
exclude = exclude.replace(os.path.sep, '/')
if exclude.startswith('/'):
exclude = RemoveTrailingSep(source) + exclude
parts = exclude.rsplit('/', 1)
if len(parts) == 1:
regexes.append(RegularExpression.WildcardSearchToRegularExpression(parts[-1].replace('/', os.path.sep)))
else:
regexes.append(( RegularExpression.WildcardSearchToRegularExpression(parts[0].replace('/', os.path.sep)),
RegularExpression.WildcardSearchToRegularExpression(parts[1].replace('/', os.path.sep)),
))
to_ignore = {}
num_roots = 0
for root, dirs, items in os.walk(source):
this_to_ignore = set()
for collection in [ dirs, items ]:
index = 0
while index < len(collection):
item = collection[index]
for regex in regexes:
if ( (isinstance(regex, tuple) and regex[0].match(root) and regex[1].match(item)) or
(not isinstance(regex, tuple) and regex.match(item))
):
this_to_ignore.add(item)
item = None
break
if item is None:
del collection[index]
else:
index += 1
if this_to_ignore:
to_ignore[root] = this_to_ignore
if dirs or items:
num_roots += 1
with tqdm.tqdm( total=num_roots,
file=StreamDecorator(output_stream),
ncols=120,
unit=" directories",
) as progress:
# ----------------------------------------------------------------------
def IgnoreFunc(root, items):
if root in to_ignore:
this_to_ignore = to_ignore[root]
index = 0
while index < len(items):
if items[index] in this_to_ignore:
del items[index]
else:
index += 1
if items:
progress.update(1)
return root, items
# ----------------------------------------------------------------------
shutil.copytree(source, dest, ignore=IgnoreFunc)
# ----------------------------------------------------------------------
def RemoveTree( path,
optional_retry_iterations=5,
):
if not os.path.isdir(path):
return False
from CommonEnvironment import Shell
environment = Shell.GetEnvironment()
_RemoveImpl(environment.RemoveDir, path, optional_retry_iterations)
return True
# ----------------------------------------------------------------------
def RemoveFile( path,
optional_retry_iterations=5, # Can be None
):
if not os.path.isfile(path):
return False
_RemoveImpl(os.remove, path, optional_retry_iterations)
return True
# ----------------------------------------------------------------------
def MakeDirs(path):
if not os.path.isdir(path):
os.makedirs(path)
# ---------------------------------------------------------------------------
# ---------------------------------------------------------------------------
# ---------------------------------------------------------------------------
def _ProcessWalkArgs(include_items, exclude_items):
# ---------------------------------------------------------------------------
def Preprocess(items):
if items == None:
return []
if isinstance(items, list):
return items
return [ items, ]
# ---------------------------------------------------------------------------
def In(value, items):
for item in items:
if isinstance(item, str) and item == value:
return True
elif callable(item):
try:
if item(value):
return True
except:
pass
elif hasattr(item, "match") and item.match(value):
return True
return False
# ---------------------------------------------------------------------------
include_items = Preprocess(include_items)
exclude_items = Preprocess(exclude_items)
# ---------------------------------------------------------------------------
def Impl(value):
if exclude_items and In(value, exclude_items):
return False
if include_items and not In(value, include_items):
return False
return True
# ---------------------------------------------------------------------------
return Impl
# ---------------------------------------------------------------------------
def _RemoveImpl( func, # def Func(renamed_path)
path,
optional_retry_iterations,
):
assert os.path.exists(path), path
# Rename the dir or item to a temporary one and then remove
# the renamed item. This works around timing issues associated
# with quickly creating an item after it has just been deleted.
iteration = 0
while True:
potential_renamed_path = "{}_ToDelete{}".format(path, iteration)
if not os.path.exists(potential_renamed_path):
renamed_path = potential_renamed_path
break
iteration += 1
# Invoke
iteration = 0
while True:
try:
os.rename(path, renamed_path)
break
except:
if optional_retry_iterations != None:
# Handle temporary permission denied errors by retrying after a
# period of time.
time.sleep(1) # seconds
iteration += 1
if iteration < optional_retry_iterations:
continue
raise
func(renamed_path)
|
"""
Plot composite periods for LRP between experiments
Reference : Deser et al. [2020, JCLI]
Author : Zachary M. Labe
Date : 5 April 2021
Version : R1
"""
### Import packages
import math
import time
import matplotlib.pyplot as plt
import numpy as np
from netCDF4 import Dataset
import scipy.stats as sts
from mpl_toolkits.basemap import Basemap, addcyclic, shiftgrid
import palettable.cubehelix as cm
import calc_Utilities as UT
import calc_dataFunctions as df
import itertools
###############################################################################
###############################################################################
###############################################################################
### Data preliminaries
directorydata = '/Users/zlabe/Documents/Research/InternalSignal/Data/FINAL/'
directoryfigure = '/Users/zlabe/Desktop/PAPER/R1/'
datasetsingleq = np.repeat(['AER+','GHG+','ALL'],4)
datasetsingle = ['XGHG','XAER','lens']
timeq = ['1920-1959','1960-1999','2000-2039','2040-2079']
seasons = ['annual','JFM','AMJ','JAS','OND']
letters = ["a","b","c","d","e","f","g","h","i","j","k","l","m"]
years = np.arange(1920,2079+1,1)
variables = ['T2M']
monthlychoice = seasons[0]
reg_name = 'Globe'
SAMPLEQ = 100
### Read in LRP maps (XGHG)
data = Dataset(directorydata + 'LRP_Maps_XGHG_AllSeasons_PAPER.nc')
lat1 = data.variables['lat'][:]
lon1 = data.variables['lon'][:]
lrp_ghg = data.variables['LRP'][:]
data.close()
lrpghg = lrp_ghg[0]
### Read in LRP maps (XAER)
data = Dataset(directorydata + 'LRP_Maps_XAER_AllSeasons_PAPER.nc')
lat1 = data.variables['lat'][:]
lon1 = data.variables['lon'][:]
lrp_aer = data.variables['LRP'][:]
data.close()
lrpaer = lrp_aer[0]
### Read in LRP maps (LENS)
data = Dataset(directorydata + 'LRP_Maps_lens_AllSeasons_PAPER.nc')
lat1 = data.variables['lat'][:]
lon1 = data.variables['lon'][:]
lrp_lens = data.variables['LRP'][:]
data.close()
lrplens = lrp_lens[0]
### Procress time
comp_ghg = np.empty((len(years)//40,lrpghg.shape[1],lrpghg.shape[2]))
comp_aer = np.empty((len(years)//40,lrpaer.shape[1],lrpaer.shape[2]))
comp_lens = np.empty((len(years)//40,lrplens.shape[1],lrplens.shape[2]))
for count,i in enumerate(range(0,len(years),40)):
comp_ghg[count,:,:,] = np.nanmean(lrpghg[i:i+40,:,:],axis=0)
comp_aer[count,:,:,] = np.nanmean(lrpaer[i:i+40,:,:],axis=0)
comp_lens[count,:,:,] = np.nanmean(lrplens[i:i+40,:,:],axis=0)
thresh = np.genfromtxt(directorydata + 'Threshold_MaskingLRP_95.txt',
unpack=True)
comp_ghgm = comp_ghg.copy()
comp_aerm = comp_aer.copy()
comp_lensm = comp_lens.copy()
comp_ghg[comp_ghg<=thresh] = np.nan
comp_aer[comp_aer<=thresh] = np.nan
comp_lens[comp_lens<=thresh] = np.nan
runs = list(itertools.chain.from_iterable([comp_ghg,comp_aer,comp_lens]))
runsm = list(itertools.chain.from_iterable([comp_ghgm,comp_aerm,comp_lensm]))
###########################################################################
###########################################################################
###########################################################################
### Plot variable data for trends
plt.rc('text',usetex=True)
plt.rc('font',**{'family':'sans-serif','sans-serif':['Avant Garde']})
### Set limits for contours and colorbars
limit = np.arange(0,0.5001,0.005)
barlim = np.round(np.arange(0,0.6,0.1),2)
cmap = cm.classic_16.mpl_colormap
label = r'\textbf{RELEVANCE}'
fig = plt.figure(figsize=(5,3))
for r in range(len(runs)):
var = runs[r]
ax1 = plt.subplot(3,4,r+1)
m = Basemap(projection='moll',lon_0=0,resolution='l',area_thresh=10000)
circle = m.drawmapboundary(fill_color='dimgrey')
circle.set_clip_on(False)
m.drawcoastlines(color='darkgrey',linewidth=0.27)
var, lons_cyclic = addcyclic(var, lon1)
var, lons_cyclic = shiftgrid(180., var, lons_cyclic, start=False)
lon2d, lat2d = np.meshgrid(lons_cyclic, lat1)
x, y = m(lon2d, lat2d)
circle = m.drawmapboundary(fill_color='dimgrey',color='dimgray',
linewidth=0.7)
circle.set_clip_on(False)
cs = m.contourf(x,y,var,limit,extend='max')
cs.set_cmap(cmap)
if any([r==0,r==4,r==8]):
ax1.annotate(r'\textbf{%s}' % datasetsingleq[r],xy=(0,0),xytext=(-0.1,0.5),
textcoords='axes fraction',color='k',fontsize=9,
rotation=90,ha='center',va='center')
if any([r==0,r==1,r==2,r==3]):
ax1.annotate(r'\textbf{%s}' % timeq[r],xy=(0,0),xytext=(0.5,1.22),
textcoords='axes fraction',color='dimgrey',fontsize=9,
rotation=0,ha='center',va='center')
ax1.annotate(r'\textbf{[%s]}' % letters[r],xy=(0,0),xytext=(0.87,0.97),
textcoords='axes fraction',color='k',fontsize=6,
rotation=330,ha='center',va='center')
###########################################################################
cbar_ax = fig.add_axes([0.32,0.095,0.4,0.03])
cbar = fig.colorbar(cs,cax=cbar_ax,orientation='horizontal',
extend='max',extendfrac=0.07,drawedges=False)
cbar.set_label(label,fontsize=9,color='dimgrey',labelpad=1.4)
cbar.set_ticks(barlim)
cbar.set_ticklabels(list(map(str,barlim)))
cbar.ax.tick_params(axis='x', size=.01,labelsize=5)
cbar.outline.set_edgecolor('dimgrey')
plt.tight_layout()
plt.subplots_adjust(top=0.85,wspace=0.01,hspace=0,bottom=0.14)
plt.savefig(directoryfigure + 'LRPPeriods_T2M_PAPER.png',dpi=600)
###########################################################################
###########################################################################
###########################################################################
fig = plt.figure(figsize=(5,3))
for r in range(len(runs)):
var = runsm[r]
ax1 = plt.subplot(3,4,r+1)
m = Basemap(projection='moll',lon_0=0,resolution='l',area_thresh=10000)
circle = m.drawmapboundary(fill_color='dimgrey')
circle.set_clip_on(False)
m.drawcoastlines(color='darkgrey',linewidth=0.27)
var, lons_cyclic = addcyclic(var, lon1)
var, lons_cyclic = shiftgrid(180., var, lons_cyclic, start=False)
lon2d, lat2d = np.meshgrid(lons_cyclic, lat1)
x, y = m(lon2d, lat2d)
circle = m.drawmapboundary(fill_color='dimgrey',color='dimgray',
linewidth=0.7)
circle.set_clip_on(False)
cs = m.contourf(x,y,var,limit,extend='max')
cs.set_cmap(cmap)
if any([r==0,r==4,r==8]):
ax1.annotate(r'\textbf{%s}' % datasetsingleq[r],xy=(0,0),xytext=(-0.1,0.5),
textcoords='axes fraction',color='k',fontsize=9,
rotation=90,ha='center',va='center')
if any([r==0,r==1,r==2,r==3]):
ax1.annotate(r'\textbf{%s}' % timeq[r],xy=(0,0),xytext=(0.5,1.22),
textcoords='axes fraction',color='dimgrey',fontsize=9,
rotation=0,ha='center',va='center')
ax1.annotate(r'\textbf{[%s]}' % letters[r],xy=(0,0),xytext=(0.87,0.97),
textcoords='axes fraction',color='k',fontsize=6,
rotation=330,ha='center',va='center')
###########################################################################
cbar_ax = fig.add_axes([0.32,0.095,0.4,0.03])
cbar = fig.colorbar(cs,cax=cbar_ax,orientation='horizontal',
extend='max',extendfrac=0.07,drawedges=False)
cbar.set_label(label,fontsize=9,color='dimgrey',labelpad=1.4)
cbar.set_ticks(barlim)
cbar.set_ticklabels(list(map(str,barlim)))
cbar.ax.tick_params(axis='x', size=.01,labelsize=5)
cbar.outline.set_edgecolor('dimgrey')
plt.tight_layout()
plt.subplots_adjust(top=0.85,wspace=0.01,hspace=0,bottom=0.14)
plt.savefig(directoryfigure + 'LRPPeriods_T2M_NOMASK.png',dpi=600)
|
from imdb import IMDB
from imagenet_vid import TwitchVID
|
import logging
import src.core.config as config
from functools import wraps
from src.main import logger, get_resource
from src.core.request import Request
from src.core.response import response
from src.core.request import DEBUG_HEADER
def api_endpoint():
"""Decorate a lambda function endpoint with user access checking"""
def decorator(func):
@wraps(func)
def decorated(event, context):
try:
# Create ApiRequest layer and init context
# Get DB Session
resource = get_resource()
req = Request(event=event, aws_request_id=context.aws_request_id, resource=resource)
req.set_request_context()
# Assign request to context
context.request = req
# Update logging level
if DEBUG_HEADER in config.global_context and config.global_context[DEBUG_HEADER] == 'true':
logger.setLevel(logging.DEBUG)
else:
logger.setLevel(logging.INFO)
# Call method and manage session in case of error
err, res = func(event, context, resource)
except Exception as e:
logger.error(e)
err, res = e, None
err.status_code = '500'
return response(err, res)
return decorated
return decorator
|
'''
Author: Junbong Jang
6/10/2020
Automatically get the edge from the images to aid human labelers
'''
import matplotlib
matplotlib.use('Agg') # Must be before importing matplotlib.pyplot or pylab!
import cv2
import numpy as np
from skimage import io
import matplotlib.pyplot as plt
import glob
import os
from PIL import Image
from scipy import ndimage
from cv2.ximgproc import guidedFilter
# from cv2_rolling_ball import subtract_background_rolling_ball
# import bm3d
import user_params
from visualization_helper import *
# ------------ Image Processing Algorithms -------------------------
# https://www.pyimagesearch.com/2015/04/06/zero-parameter-automatic-canny-edge-detection-with-python-and-opencv/
def auto_canny(image, canny_std_multiplier):
img_mean = np.average(image)
img_std = np.std(image)
lower = max(0, img_mean - (canny_std_multiplier+1)*img_std)
upper = max(0, img_mean - canny_std_multiplier*img_std)
# print('auto_canny:', img_mean, img_std, lower, upper)
edges = cv2.Canny(image, lower, upper, 3, L2gradient=True)
return edges
def clean_edge(input_edge):
cleaned_edge = input_edge.copy()
# Filter using contour area and remove small noise
# https://stackoverflow.com/questions/60033274/how-to-remove-small-object-in-image-with-python
cnts = cv2.findContours(cleaned_edge, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)
cnts = cnts[0] if len(cnts) == 2 else cnts[1]
counter = 0
for c in cnts:
area = cv2.contourArea(c)
perimeter = cv2.arcLength(c,False)
if perimeter < 100:
counter = counter + 1
contour_cmap = (0,0,0)
cv2.drawContours(cleaned_edge, [c], -1, contour_cmap, -1)
'''
elif area > 0:
contour_cmap = (255,255,255)
cv2.drawContours(cleaned_edge, [c], -1, contour_cmap, -1)
'''
print('number of deleted small edge:', str(counter))
return cleaned_edge
def denoise_image(img, denoise_option, denoise_kernel_size):
if denoise_option=='bm3d':
denoised_image = bm3d.bm3d(img, sigma_psd=30/255, stage_arg=bm3d.BM3DStages.ALL_STAGES) # .
denoised_image = np.around(denoised_image,0).astype(np.uint8)#convert float to uint8
elif denoise_option=='bilat':
denoised_image = cv2.bilateralFilter(img,denoise_kernel_size,75,75)
elif denoise_option=='median':
denoised_image = cv2.medianBlur(img,denoise_kernel_size)
elif denoise_option=='guided':
r = 2; # try r=2, 4, or 8
eps = 0.4 * 0.4; # try eps=0.1^2, 0.2^2, 0.4^2
eps *= 255 * 255; # Because the intensity range of our images is [0, 255]
denoised_image = guidedFilter(img,img,r,eps)
elif denoise_option=='gauss':
denoised_image = cv2.blur(img, (denoise_kernel_size,denoise_kernel_size))
elif denoise_option=='kuwahara':
denoised_image = Kuwahara(img, 13)
else:
denoised_image = None
return denoised_image
def extract_edge(img, denoise_option, canny_std_multiplier, denoise_kernel_size, debug_mode):
denoised_image = denoise_image(img, denoise_option, denoise_kernel_size)
# subtracted_img, background = subtract_background_rolling_ball(denoised_image.copy(), 30, light_background=False, use_paraboloid=True, do_presmooth=False)
canny_edge = auto_canny(denoised_image, canny_std_multiplier)
# connects fragmented line one pixel away
kernel = np.ones((2,2),np.uint8)
dilated_canny_edge = cv2.dilate(canny_edge,kernel,iterations = 1)
eroded_canny_edge = cv2.erode(dilated_canny_edge,kernel,iterations = 1)
cleaned_edge = clean_edge(eroded_canny_edge)
# --------
if debug_mode:
im = Image.fromarray(background)
im.save('background_{}.png'.format(denoise_option))
im = Image.fromarray(denoised_image)
im.save('denoised_image_{}.png'.format(denoise_option))
im = Image.fromarray(canny_edge)
im.save('canny_edge_{}.png'.format(denoise_option))
im = Image.fromarray(cleaned_edge)
im.save('cleaned_edge_{}.png'.format(denoise_option))
return cleaned_edge
def extract_edges(img, img_name, edge_path, canny_std_multiplier, denoise_kernel_size):
# get edge from the image
#bilat_edge = extract_edge(img, denoise_option='bilat', canny_std_multiplier, denoise_kernel_size, debug_mode=False)
#gauss_edge = extract_edge(img, denoise_option='gauss', canny_std_multiplier, denoise_kernel_size, debug_mode=False)
guided_edge = extract_edge(img, 'guided', canny_std_multiplier, denoise_kernel_size, debug_mode=False)
# added_edge = gauss_edge + bilat_edge + guided_edge
added_edge = guided_edge
im = Image.fromarray(added_edge)
im.save(edge_path + '/' + img_name)
# orig image and edge overlaid image side by side
save_path = edge_path + '/overlay_' + img_name
overlaid_img = overlay_edge_over_img(img, added_edge, save_path='')
visualize_two_images_side_by_side(img, overlaid_img, save_path)
def visualize_two_images_side_by_side(img, overlaid_img, save_path):
f, axarr = plt.subplots(1,2)
axarr[0].imshow(img, cmap = 'gray')
axarr[0].axis('off')
axarr[1].imshow(overlaid_img)
axarr[1].axis('off')
plt.tight_layout(pad=0.2) # remove the padding between images
plt.savefig(save_path, bbox_inches = 'tight', pad_inches = 0, dpi=240) # remove up and down paddings
plt.close()
if __name__ == "__main__":
if not os.path.exists(user_params.saved_edge_path):
os.makedirs(user_params.saved_edge_path)
# get all of dataset's images
img_list = glob.glob(user_params.img_root_path + '*' + '.png')
print('number of images: ', len(img_list))
# extract edge for each original image
for img_index in range(len(img_list)):
# Get an image and its name
img_path = img_list[img_index]
img = cv2.imread(img_path,cv2.IMREAD_GRAYSCALE)
img_name = img_path[len(user_params.img_root_path):]
print(img_name, img.shape)
extract_edges(img, img_name, user_params.saved_edge_path, user_params.canny_std_multiplier, user_params.denoise_kernel_size)
|
from .General_Core import SparCC_MicNet
__all__=['SparCC_MicNet'] |
# coding: utf-8
from __future__ import unicode_literals
import json
class WxBot(object):
"""
储存微信 bot 相关信息及 wechat_sender 各类 receiver 的类
"""
def __new__(cls, *args, **kwargs):
if not hasattr(cls, '_instance'):
orig = super(WxBot, cls)
cls._instance = orig.__new__(cls)
return cls._instance
def __init__(self, bot=None, receivers=None, status_receiver=None, *args, **kwargs):
"""
:param bot: wxpy bot 对象实例
:param receivers: wxpy chat 对象实例
:param status_receiver: wxpy chat 对象实例
"""
self.bot = bot
self.receivers = {}
self.default_receiver = None
self.init_receivers(receivers)
self.status_receiver = status_receiver if status_receiver else self.default_receiver
self.receivers['status'] = self.status_receiver
super(WxBot, self).__init__(*args, **kwargs)
def init_receivers(self, receivers):
"""
初始化 receivers
"""
if not receivers:
self.default_receiver = self.bot.file_helper
return True
if isinstance(receivers, list):
self.default_receiver = receivers[0]
for receiver in receivers:
if self.bot.puid_map:
self.receivers[receiver.puid] = receiver
self.receivers[receiver.name] = receiver
else:
self.default_receiver = receivers
if self.bot.puid_map:
self.receivers[receivers.puid] = receivers
self.receivers[receivers.name] = receivers
def send_msg(self, msg):
"""
wxpy 发送文本消息的基本封装，这里会进行消息 receiver 识别分发
"""
for receiver in msg.receivers:
current_receiver = self.receivers.get(receiver, self.default_receiver)
current_receiver.send_msg(msg)
class Message(object):
"""
wechat_sender 消息类，是所有 wechat_sender 发送消息的基本类型
"""
def __init__(self, content, title=None, time=None, remind=None, interval=None, receivers=None):
"""
:param content: 消息内容
:param title: 消息标题
:param time: 消息时间
:param remind: 消息提醒时间
:param interval: 消息提醒间隔
:param receivers: 消息接收者
"""
self.title = title
self.content = content
self.message_time = time
self.remind_time = None
if time and remind:
self.remind_time = time - remind
self.nc = remind
self.message_interval = interval
self.receivers = [itm for itm in receivers.split(',')] if receivers else ['default']
@property
def time(self):
"""
:return: 以字符串 "xxxx-xx-xx xx:xx:xx" 的形式返回消息的时间
"""
return self.message_time.strftime('%Y-%m-%d %H:%M:%S') if self.message_time else None
@property
def interval(self):
"""
:return: 返回消息提醒间隔的秒数
"""
return '{0}s'.format(self.message_interval.seconds) if self.message_interval else None
@property
def remind(self):
"""
:return: 以字符串 "xxxx-xx-xx xx:xx:xx" 的形式返回消息的提醒时间
"""
return self.remind_time.strftime('%Y-%m-%d %H:%M:%S') if self.message_time else None
def render_message(self):
"""
渲染消息
:return: 渲染后的消息
"""
message = None
if self.title:
message = '标题：{0}'.format(self.title)
if self.message_time:
message = '{0}\n时间：{1}'.format(message, self.time)
if message:
message = '{0}\n内容：{1}'.format(message, self.content)
else:
message = self.content
return message
def __repr__(self):
return self.render_message()
class Global(object):
"""
wechat_sender 的全局对象类
"""
def __new__(cls, *args, **kwargs):
if not hasattr(cls, '_instance'):
orig = super(Global, cls)
cls._instance = orig.__new__(cls)
return cls._instance
def __init__(self, *args, **kwargs):
for k, v in kwargs.items():
setattr(self, k, v)
def insert(self, name, value):
setattr(self, name, value)
return True
def __call__(self, *args, **kwargs):
return self.__dict__
|
#!/usr/bin/python
# -*- coding: utf-8 -*-
from __future__ import absolute_import
from six.moves import range
from functools import reduce
__author__ = 'Austin Taylor'
from ..base.config import vwConfig
import pandas as pd
from lxml import objectify
import sys
import os
import io
import time
import sqlite3
import json
import logging
import socket
from datetime import datetime
class vulnWhispererBase(object):
CONFIG_SECTION = None
def __init__(
self,
config=None,
db_name='report_tracker.db',
section=None,
purge=False,
verbose=False
):
if self.CONFIG_SECTION is None:
raise Exception('Implementing class must define CONFIG_SECTION')
self.exit_code = 0
self.db_name = db_name
self.purge = purge
# set up logger
self.logger = logging.getLogger('vulnWhispererBase')
if verbose:
self.logger.setLevel(logging.DEBUG)
# if the config is available
if config is not None:
self.config = vwConfig(config_in=config)
try:
self.enabled = self.config.get(self.CONFIG_SECTION, 'enabled')
except:
self.enabled = False
self.write_path = self.config.get(self.CONFIG_SECTION, 'write_path')
self.db_path = self.config.get(self.CONFIG_SECTION, 'db_path')
if self.db_name is not None:
if self.db_path:
self.database = os.path.join(self.db_path,
db_name)
else:
self.database = \
os.path.abspath(os.path.join(os.path.dirname(__file__),
'database', db_name))
if not os.path.exists(self.db_path):
os.makedirs(self.db_path)
self.logger.info('Creating directory {dir}'.format(dir=self.db_path))
if not os.path.exists(self.database):
with open(self.database, 'w'):
self.logger.info('Creating file {dir}'.format(dir=self.database))
try:
self.conn = sqlite3.connect(self.database)
self.cur = self.conn.cursor()
self.logger.info('Connected to database at {loc}'.format(loc=self.database))
except Exception as e:
self.logger.error(
'Could not connect to database at {loc}\nReason: {e} - Please ensure the path exist'.format(
e=e,
loc=self.database))
else:
self.logger.error('Please specify a database to connect to!')
exit(1)
self.table_columns = [
'scan_name',
'scan_id',
'last_modified',
'filename',
'download_time',
'record_count',
'source',
'uuid',
'processed',
'reported',
]
self.init()
self.uuids = self.retrieve_uuids()
self.processed = 0
self.skipped = 0
self.scan_list = []
def create_table(self):
self.cur.execute(
'CREATE TABLE IF NOT EXISTS scan_history (id INTEGER PRIMARY KEY,'
' scan_name TEXT, scan_id INTEGER, last_modified DATE, filename TEXT,'
' download_time DATE, record_count INTEGER, source TEXT,'
' uuid TEXT, processed INTEGER, reported INTEGER)'
)
self.conn.commit()
def delete_table(self):
self.cur.execute('DELETE FROM scan_history WHERE source=\'{}\''.format(self.CONFIG_SECTION))
self.conn.commit()
def init(self):
if self.purge:
self.logger.info('Requested purge of {} data.'.format(self.CONFIG_SECTION))
self.delete_table()
self.create_table()
def cleanser(self, _data):
repls = (('\n', r'\n'), ('\r', r'\r'))
data = reduce(lambda a, kv: a.replace(*kv), repls, _data)
return data
def path_check(self, _data):
if self.write_path:
if '/' or '\\' in _data[-1]:
data = self.write_path + _data
else:
data = self.write_path + '/' + _data
return data
def record_insert(self, record):
# for backwards compatibility with older versions without "reported" field
try:
# -1 to get the latest column, 1 to get the column name (old version would be "processed", new "reported")
# TODO delete backward compatibility check after some versions
last_column_table = self.cur.execute('PRAGMA table_info(scan_history)').fetchall()[-1][1]
if last_column_table == self.table_columns[-1]:
self.cur.execute('insert into scan_history({table_columns}) values (?,?,?,?,?,?,?,?,?,?)'.format(
table_columns=', '.join(self.table_columns)), record)
else:
self.cur.execute('insert into scan_history({table_columns}) values (?,?,?,?,?,?,?,?,?)'.format(
table_columns=', '.join(self.table_columns[:-1])), record[:-1])
self.conn.commit()
except Exception as e:
self.logger.error("Failed to insert record in database. Error: {}".format(e))
sys.exit(1)
def retrieve_uuids(self):
"""
Retrieves UUIDs from database and checks list to determine which files need to be processed.
:return:
"""
try:
self.conn.text_factory = str
self.cur.execute('SELECT uuid FROM scan_history where source = "{config_section}"'.format(
config_section=self.CONFIG_SECTION))
results = frozenset([r[0] for r in self.cur.fetchall()])
except:
results = []
return results
|
from django.core.management.base import BaseCommand, CommandError
from bankruptcy.cases.models import Case, DocketEntry, Document
class Command(BaseCommand):
help = 'Consolidate entities'
def handle (sself, *args, **options):
cases = Case.objects.all()
case_count = cases.count()
for i, case in enumerate(cases.iterator(chunksize=10)):
print(f'Consolidating case {i} / {case_count}.')
for de in case.docket_entries.all():
for doc in de.documents.all():
case.entities.add(*(doc.entities.names()))
|
#!/usr/bin/env python
# vim: set fileencoding=utf-8 :
import os
from bob.pipelines import DelayedSample, SampleSet
from bob.db.base.utils import check_parameters_for_validity
import csv
import bob.io.base
import functools
import numpy as np
import itertools
import logging
import bob.db.base
from bob.bio.base.pipelines.vanilla_biometrics.abstract_classes import Database
from bob.extension.download import search_file, list_dir
from bob.pipelines.sample_loaders import CSVToSampleLoader
logger = logging.getLogger(__name__)
def convert_samples_to_samplesets(samples, group_by_reference_id=True, references=None):
if group_by_reference_id:
# Grouping sample sets
sample_sets = dict()
for s in samples:
if s.reference_id not in sample_sets:
sample_sets[s.reference_id] = (
SampleSet([s], parent=s)
if references is None
else SampleSet([s], parent=s, references=references)
)
else:
sample_sets[s.reference_id].append(s)
return list(sample_sets.values())
else:
return (
[SampleSet([s], parent=s) for s in samples]
if references is None
else [SampleSet([s], parent=s, references=references) for s in samples]
)
class LSTToSampleLoader(CSVToSampleLoader):
"""
Simple mechanism that converts the lines of a LST file to
:any:`bob.pipelines.DelayedSample` or :any:`bob.pipelines.SampleSet`
"""
def transform(self, X):
X.seek(0)
reader = csv.reader(X, delimiter=" ")
samples = []
for row in reader:
if row[0][0] == "#":
continue
samples.append(self.convert_row_to_sample(row))
return samples
def convert_row_to_sample(self, row, header=None):
if len(row) == 4:
path = row[0]
compare_reference_id = row[1]
reference_id = str(row[3])
kwargs = {"compare_reference_id": str(compare_reference_id)}
else:
path = row[0]
reference_id = str(row[1])
kwargs = dict()
if len(row) == 3:
subject = row[2]
kwargs = {"subject_id": str(subject)}
return DelayedSample(
functools.partial(
self.data_loader,
os.path.join(self.dataset_original_directory, path + self.extension),
),
key=path,
reference_id=reference_id,
**kwargs,
)
class CSVToSampleLoaderBiometrics(CSVToSampleLoader):
"""
Base class that converts the lines of a CSV file, like the one below to
:any:`bob.pipelines.DelayedSample` or :any:`bob.pipelines.SampleSet`
.. code-block:: text
PATH,REFERENCE_ID
path_1,reference_id_1
path_2,reference_id_2
path_i,reference_id_j
...
Parameters
----------
data_loader:
A python function that can be called parameterlessly, to load the
sample in question from whatever medium
dataset_original_directory: str
Path of where data is stored
extension: str
Default file extension
"""
def __init__(
self,
data_loader,
dataset_original_directory="",
extension="",
reference_id_equal_subject_id=True,
):
super().__init__(
data_loader=data_loader,
extension=extension,
dataset_original_directory=dataset_original_directory,
)
self.reference_id_equal_subject_id = reference_id_equal_subject_id
def convert_row_to_sample(self, row, header):
path = row[0]
reference_id = row[1]
kwargs = dict([[str(h).lower(), r] for h, r in zip(header[2:], row[2:])])
if self.reference_id_equal_subject_id:
kwargs["subject_id"] = reference_id
else:
if "subject_id" not in kwargs:
raise ValueError(f"`subject_id` not available in {header}")
return DelayedSample(
functools.partial(
self.data_loader,
os.path.join(self.dataset_original_directory, path + self.extension),
),
key=path,
reference_id=reference_id,
**kwargs,
)
class CSVDataset(Database):
"""
Generic filelist dataset for :any:` bob.bio.base.pipelines.vanilla_biometrics.VanillaBiometricsPipeline` pipeline.
Check :any:`vanilla_biometrics_features` for more details about the Vanilla Biometrics Dataset
interface.
To create a new dataset, you need to provide a directory structure similar to the one below:
.. code-block:: text
my_dataset/
my_dataset/my_protocol/norm/train_world.csv
my_dataset/my_protocol/dev/for_models.csv
my_dataset/my_protocol/dev/for_probes.csv
my_dataset/my_protocol/eval/for_models.csv
my_dataset/my_protocol/eval/for_probes.csv
...
In the above directory structure, inside of `my_dataset` should contain the directories with all
evaluation protocols this dataset might have.
Inside of the `my_protocol` directory should contain at least two csv files:
- for_models.csv
- for_probes.csv
Those csv files should contain in each row i-) the path to raw data and ii-) the reference_id label
for enrollment (:any:`bob.bio.base.pipelines.vanilla_biometrics.Database.references`) and
probing (:any:`bob.bio.base.pipelines.vanilla_biometrics.Database.probes`).
The structure of each CSV file should be as below:
.. code-block:: text
PATH,reference_id
path_1,reference_id_1
path_2,reference_id_2
path_i,reference_id_j
...
You might want to ship metadata within your Samples (e.g gender, age, annotation, ...)
To do so is simple, just do as below:
.. code-block:: text
PATH,reference_id,METADATA_1,METADATA_2,METADATA_k
path_1,reference_id_1,A,B,C
path_2,reference_id_2,A,B,1
path_i,reference_id_j,2,3,4
...
The files `my_dataset/my_protocol/train.csv/eval_enroll.csv` and `my_dataset/my_protocol/train.csv/eval_probe.csv`
are optional and it is used in case a protocol contains data for evaluation.
Finally, the content of the file `my_dataset/my_protocol/train.csv` is used in the case a protocol
contains data for training (`bob.bio.base.pipelines.vanilla_biometrics.Database.background_model_samples`)
Parameters
----------
dataset_path: str
Absolute path or a tarball of the dataset protocol description.
protocol_na,e: str
The name of the protocol
csv_to_sample_loader: `bob.pipelines.sample_loaders.CSVToSampleLoader`
Base class that whose objective is to generate :any:`bob.pipelines.Sample`
and/or :any:`bob.pipelines.SampleSet` from csv rows
"""
def __init__(
self,
*,
name,
protocol,
dataset_protocol_path,
csv_to_sample_loader=None,
is_sparse=False,
allow_scoring_with_all_biometric_references=False,
group_probes_by_reference_id=False,
**kwargs,
):
super().__init__(
name=name,
protocol=protocol,
allow_scoring_with_all_biometric_references=allow_scoring_with_all_biometric_references,
**kwargs,
)
self.dataset_protocol_path = dataset_protocol_path
self.is_sparse = is_sparse
self.group_probes_by_reference_id = group_probes_by_reference_id
if csv_to_sample_loader is None:
csv_to_sample_loader = CSVToSampleLoaderBiometrics(
data_loader=bob.io.base.load,
dataset_original_directory="",
extension="",
)
def get_paths():
if not os.path.exists(dataset_protocol_path):
raise ValueError(f"The path `{dataset_protocol_path}` was not found")
# Here we are handling the legacy
train_csv = search_file(
dataset_protocol_path,
[
os.path.join(protocol, "norm", "train_world.lst"),
os.path.join(protocol, "norm", "train_world.csv"),
],
)
dev_enroll_csv = search_file(
dataset_protocol_path,
[
os.path.join(protocol, "dev", "for_models.lst"),
os.path.join(protocol, "dev", "for_models.csv"),
],
)
legacy_probe = "for_scores.lst" if self.is_sparse else "for_probes.lst"
dev_probe_csv = search_file(
dataset_protocol_path,
[
os.path.join(protocol, "dev", legacy_probe),
os.path.join(protocol, "dev", "for_probes.csv"),
],
)
eval_enroll_csv = search_file(
dataset_protocol_path,
[
os.path.join(protocol, "eval", "for_models.lst"),
os.path.join(protocol, "eval", "for_models.csv"),
],
)
eval_probe_csv = search_file(
dataset_protocol_path,
[
os.path.join(protocol, "eval", legacy_probe),
os.path.join(protocol, "eval", "for_probes.csv"),
],
)
# The minimum required is to have `dev_enroll_csv` and `dev_probe_csv`
# Dev
if dev_enroll_csv is None:
raise ValueError(
f"The file `{dev_enroll_csv}` is required and it was not found"
)
if dev_probe_csv is None:
raise ValueError(
f"The file `{dev_probe_csv}` is required and it was not found"
)
return (
train_csv,
dev_enroll_csv,
dev_probe_csv,
eval_enroll_csv,
eval_probe_csv,
)
(
self.train_csv,
self.dev_enroll_csv,
self.dev_probe_csv,
self.eval_enroll_csv,
self.eval_probe_csv,
) = get_paths()
def get_dict_cache():
cache = dict()
cache["train"] = None
cache["dev_enroll_csv"] = None
cache["dev_probe_csv"] = None
cache["eval_enroll_csv"] = None
cache["eval_probe_csv"] = None
return cache
self.cache = get_dict_cache()
self.csv_to_sample_loader = csv_to_sample_loader
def background_model_samples(self):
self.cache["train"] = (
self.csv_to_sample_loader.transform(self.train_csv)
if self.cache["train"] is None
else self.cache["train"]
)
return self.cache["train"]
def _get_samplesets(
self,
group="dev",
cache_key=None,
group_by_reference_id=False,
fetching_probes=False,
is_sparse=False,
):
if self.cache[cache_key] is not None:
return self.cache[cache_key]
# Getting samples from CSV
samples = self.csv_to_sample_loader.transform(self.__getattribute__(cache_key))
references = None
if fetching_probes and is_sparse:
# Checking if `is_sparse` was set properly
if len(samples) > 0 and not hasattr(samples[0], "compare_reference_id"):
ValueError(
f"Attribute `compare_reference_id` not found in `{samples[0]}`."
"Make sure this attribute exists in your dataset if `is_sparse=True`"
)
sparse_samples = dict()
for s in samples:
if s.key in sparse_samples:
sparse_samples[s.key].references.append(s.compare_reference_id)
else:
s.references = [s.compare_reference_id]
sparse_samples[s.key] = s
samples = sparse_samples.values()
else:
if fetching_probes:
references = list(
set([s.reference_id for s in self.references(group=group)])
)
sample_sets = convert_samples_to_samplesets(
samples,
group_by_reference_id=group_by_reference_id,
references=references,
)
self.cache[cache_key] = sample_sets
return self.cache[cache_key]
def references(self, group="dev"):
cache_key = "dev_enroll_csv" if group == "dev" else "eval_enroll_csv"
return self._get_samplesets(
group=group, cache_key=cache_key, group_by_reference_id=True
)
def probes(self, group="dev"):
cache_key = "dev_probe_csv" if group == "dev" else "eval_probe_csv"
return self._get_samplesets(
group=group,
cache_key=cache_key,
group_by_reference_id=self.group_probes_by_reference_id,
fetching_probes=True,
is_sparse=self.is_sparse,
)
def all_samples(self, groups=None):
"""
Reads and returns all the samples in `groups`.
Parameters
----------
groups: list or None
Groups to consider ('train', 'dev', and/or 'eval'). If `None` is
given, returns the samples from all groups.
Returns
-------
samples: list
List of :class:`bob.pipelines.Sample` objects.
"""
valid_groups = ["train"]
if self.dev_enroll_csv and self.dev_probe_csv:
valid_groups.append("dev")
if self.eval_enroll_csv and self.eval_probe_csv:
valid_groups.append("eval")
groups = list(
check_parameters_for_validity(
parameters=groups,
parameter_description="groups",
valid_parameters=valid_groups,
default_parameters=valid_groups,
)
)
samples = []
# Get train samples (background_model_samples returns a list of samples)
if "train" in groups:
samples = samples + self.background_model_samples()
groups.remove("train")
# Get enroll and probe samples
for group in groups:
for purpose in ("enroll", "probe"):
label = f"{group}_{purpose}_csv"
samples = samples + self.csv_to_sample_loader.transform(
self.__getattribute__(label)
)
return samples
def groups(self):
"""This function returns the list of groups for this database.
Returns
-------
[str]
A list of groups
"""
# We always have dev-set
groups = ["dev"]
if self.train_csv is not None:
groups.append("train")
if self.eval_enroll_csv is not None:
groups.append("eval")
return groups
def protocols(self):
return list_dir(self.dataset_protocol_path, folders=True, files=False)
class CSVDatasetZTNorm(CSVDataset):
"""
Generic filelist dataset for :any:`bob.bio.base.pipelines.vanilla_biometrics.ZTNormPipeline` pipelines.
Check :any:`vanilla_biometrics_features` for more details about the Vanilla Biometrics Dataset
interface.
This dataset interface takes as in put a :any:`CSVDataset` as input and have two extra methods:
:any:`CSVDatasetZTNorm.zprobes` and :any:`CSVDatasetZTNorm.treferences`.
To create a new dataset, you need to provide a directory structure similar to the one below:
.. code-block:: text
my_dataset/
my_dataset/my_protocol/norm/train_world.csv
my_dataset/my_protocol/norm/for_znorm.csv
my_dataset/my_protocol/norm/for_tnorm.csv
my_dataset/my_protocol/dev/for_models.csv
my_dataset/my_protocol/dev/for_probes.csv
my_dataset/my_protocol/eval/for_models.csv
my_dataset/my_protocol/eval/for_probes.csv
Parameters
----------
database: :any:`CSVDataset`
:any:`CSVDataset` to be aggregated
"""
def __init__(self, **kwargs):
super().__init__(**kwargs)
# create_cache
self.cache["znorm_csv"] = None
self.cache["tnorm_csv"] = None
znorm_csv = search_file(
self.dataset_protocol_path,
[
os.path.join(self.protocol, "norm", "for_znorm.lst"),
os.path.join(self.protocol, "norm", "for_znorm.csv"),
],
)
tnorm_csv = search_file(
self.dataset_protocol_path,
[
os.path.join(self.protocol, "norm", "for_tnorm.lst"),
os.path.join(self.protocol, "norm", "for_tnorm.csv"),
],
)
if znorm_csv is None:
raise ValueError(
f"The file `for_znorm.lst` is required and it was not found in `{self.protocol}/norm` "
)
if tnorm_csv is None:
raise ValueError(
f"The file `for_tnorm.csv` is required and it was not found `{self.protocol}/norm`"
)
self.znorm_csv = znorm_csv
self.tnorm_csv = tnorm_csv
def zprobes(self, group="dev", proportion=1.0):
if proportion <= 0 or proportion > 1:
raise ValueError(
f"Invalid proportion value ({proportion}). Values allowed from [0-1]"
)
cache_key = "znorm_csv"
samplesets = self._get_samplesets(
group=group,
cache_key=cache_key,
group_by_reference_id=self.group_probes_by_reference_id,
fetching_probes=True,
is_sparse=False,
)
zprobes = samplesets[: int(len(samplesets) * proportion)]
return zprobes
def treferences(self, covariate="sex", proportion=1.0):
if proportion <= 0 or proportion > 1:
raise ValueError(
f"Invalid proportion value ({proportion}). Values allowed from [0-1]"
)
cache_key = "tnorm_csv"
samplesets = self._get_samplesets(
group="dev",
cache_key=cache_key,
group_by_reference_id=True,
)
treferences = samplesets[: int(len(samplesets) * proportion)]
return treferences
class CSVDatasetCrossValidation(Database):
"""
Generic filelist dataset for :any:`bob.bio.base.pipelines.vanilla_biometrics.VanillaBiometricsPipeline` pipeline that
handles **CROSS VALIDATION**.
Check :any:`vanilla_biometrics_features` for more details about the Vanilla Biometrics Dataset
interface.
This interface will take one `csv_file` as input and split into i-) data for training and
ii-) data for testing.
The data for testing will be further split in data for enrollment and data for probing.
The input CSV file should be casted in the following format:
.. code-block:: text
PATH,reference_id
path_1,reference_id_1
path_2,reference_id_2
path_i,reference_id_j
...
Parameters
----------
csv_file_name: str
CSV file containing all the samples from your database
random_state: int
Pseudo-random number generator seed
test_size: float
Percentage of the reference_ids used for testing
samples_for_enrollment: float
Number of samples used for enrollment
csv_to_sample_loader: `bob.pipelines.sample_loaders.CSVToSampleLoader`
Base class that whose objective is to generate :any:`bob.pipelines.Sample`
and/or :any:`bob.pipelines.SampleSet` from csv rows
"""
def __init__(
self,
*,
name,
protocol="Default",
csv_file_name="metadata.csv",
random_state=0,
test_size=0.8,
samples_for_enrollment=1,
csv_to_sample_loader=None,
allow_scoring_with_all_biometric_references=True,
group_probes_by_reference_id=False,
**kwargs,
):
super().__init__(
name=name,
protocol=protocol,
allow_scoring_with_all_biometric_references=allow_scoring_with_all_biometric_references,
**kwargs,
)
if csv_to_sample_loader is None:
csv_to_sample_loader = CSVToSampleLoaderBiometrics(
data_loader=bob.io.base.load,
dataset_original_directory="",
extension="",
)
def get_dict_cache():
cache = dict()
cache["train"] = None
cache["dev_enroll_csv"] = None
cache["dev_probe_csv"] = None
return cache
self.random_state = random_state
self.cache = get_dict_cache()
self.csv_to_sample_loader = csv_to_sample_loader
self.csv_file_name = open(csv_file_name)
self.samples_for_enrollment = samples_for_enrollment
self.test_size = test_size
self.group_probes_by_reference_id = group_probes_by_reference_id
if self.test_size < 0 and self.test_size > 1:
raise ValueError(
f"`test_size` should be between 0 and 1. {test_size} is provided"
)
def _do_cross_validation(self):
# Shuffling samples by reference_id
samples_by_reference_id = group_samples_by_reference_id(
self.csv_to_sample_loader.transform(self.csv_file_name)
)
reference_ids = list(samples_by_reference_id.keys())
np.random.seed(self.random_state)
np.random.shuffle(reference_ids)
# Getting the training data
n_samples_for_training = len(reference_ids) - int(
self.test_size * len(reference_ids)
)
self.cache["train"] = list(
itertools.chain(
*[
samples_by_reference_id[s]
for s in reference_ids[0:n_samples_for_training]
]
)
)
# Splitting enroll and probe
self.cache["dev_enroll_csv"] = []
self.cache["dev_probe_csv"] = []
for s in reference_ids[n_samples_for_training:]:
samples = samples_by_reference_id[s]
if len(samples) < self.samples_for_enrollment:
raise ValueError(
f"Not enough samples ({len(samples)}) for enrollment for the reference_id {s}"
)
# Enrollment samples
self.cache["dev_enroll_csv"].append(
convert_samples_to_samplesets(samples[0 : self.samples_for_enrollment])[
0
]
)
self.cache["dev_probe_csv"] += convert_samples_to_samplesets(
samples[self.samples_for_enrollment :],
group_by_reference_id=self.group_probes_by_reference_id,
references=reference_ids[n_samples_for_training:],
)
def _load_from_cache(self, cache_key):
if self.cache[cache_key] is None:
self._do_cross_validation()
return self.cache[cache_key]
def background_model_samples(self):
return self._load_from_cache("train")
def references(self, group="dev"):
return self._load_from_cache("dev_enroll_csv")
def probes(self, group="dev"):
return self._load_from_cache("dev_probe_csv")
def all_samples(self, groups=None):
"""
Reads and returns all the samples in `groups`.
Parameters
----------
groups: list or None
Groups to consider ('train' and/or 'dev'). If `None` is given,
returns the samples from all groups.
Returns
-------
samples: list
List of :class:`bob.pipelines.Sample` objects.
"""
valid_groups = ["train", "dev"]
groups = check_parameters_for_validity(
parameters=groups,
parameter_description="groups",
valid_parameters=valid_groups,
default_parameters=valid_groups,
)
samples = []
# Get train samples (background_model_samples returns a list of samples)
if "train" in groups:
samples = samples + self.background_model_samples()
groups.remove("train")
# Get enroll and probe samples
for group in groups:
samples = samples + [s for s_set in self.references(group) for s in s_set]
samples = samples + [s for s_set in self.probes(group) for s in s_set]
return samples
def groups(self):
return list(("train", "dev"))
def protocols(self):
return list((self.protocol,))
def group_samples_by_reference_id(samples):
# Grouping sample sets
samples_by_reference_id = dict()
for s in samples:
if s.reference_id not in samples_by_reference_id:
samples_by_reference_id[s.reference_id] = []
samples_by_reference_id[s.reference_id].append(s)
return samples_by_reference_id
|
#!/usr/bin/env python
# -*- coding: utf-8 -*-
################################################################################
#
# qooxdoo - the new era of web development
#
# http://qooxdoo.org
#
# Copyright:
# 2006-2013 1&1 Internet AG, Germany, http://www.1und1.de
#
# License:
# MIT: https://opensource.org/licenses/MIT
# See the LICENSE file in the project's top-level directory for details.
#
# Authors:
# * Thomas Herchenroeder (thron7)
#
################################################################################
##
# Scope walker to produce a list of global identifier nodes (unfiltered).
#
##
import os, sys, re, types
from ecmascript.frontend import lang, treeutil
from ecmascript.transform.check import scopes, jshints
##
# A visitor on a Scope() tree to collect identifier nodes with global scope.
#
class GlobalsExtractor(scopes.ScopeVisitor):
def __init__(self, scope_node):
super(GlobalsExtractor, self).__init__(scope_node)
self.global_nodes = []
def visit(self, scope_node):
self.global_nodes.extend(scope_node.globals().values())
# recurse
for cld in scope_node.children:
self.visit(cld)
# - ---------------------------------------------------------------------------
##
# Extract global identifiers from the Scope() tree.
#
def scope_globals(node):
node = scopes.create_scopes(node) # update scopes
globals_getter = GlobalsExtractor(node)
globals_getter.visit(node.scope)
return globals_getter.global_nodes
# - ---------------------------------------------------------------------------
##
# Check a name against relevant jshints.
# String -> bool
#
def name_is_jsignored(name, node):
result = []
for hint in jshints.find_hints_upward(node):
for cat in (('ignore',None), ('lint','ignoreUndefined')):
if hint.ident_matches(name, cat):
result.append(cat)
return result
##
# Check an ident node against relevant jshints.
# Node -> bool
def test_ident_is_jsignored(node):
var_root = treeutil.findVarRoot(node)
name = treeutil.assembleVariable(var_root)[0]
return name_is_jsignored(name, node)
##
# Check a node against builtin symbols.
# builtins[] -> Node -> bool
def test_ident_is_builtin(builtins=lang.GLOBALS):
GlobalSymbolsCombinedPatt = re.compile('|'.join(r'^%s\b' % re.escape(x)
for x in builtins + lang.QXGLOBALS))
def test(node):
var_root = treeutil.findVarRoot(node)
name = treeutil.assembleVariable(var_root)[0]
return bool(GlobalSymbolsCombinedPatt.search(name))
return test
##
# Filter names if they match a built-in.
#
GlobalSymbolsCombinedPatt = re.compile('|'.join(r'^%s\b' % re.escape(x) for x in lang.GLOBALS + lang.QXGLOBALS))
def globals_filter_by_builtins(global_names):
return [name for name in global_names if not GlobalSymbolsCombinedPatt.search(name)]
##
# (class_names[], name_spaces[]) -> Node -> bool
def test_ident_is_libsymbol(class_names, name_spaces):
def test(node):
return test_for_libsymbol(node, class_names, name_spaces)
return test
##
# Check symbol against known classes and namespaces.
# - A known qx global is either exactly a name space, or a dotted identifier
# that is a dotted extension of a known class.
#
def test_for_libsymbol(symbol, class_names, name_spaces):
res_name = ''
# node may be unicode string or Node obj => unify
if not isinstance(symbol, unicode):
symbol = treeutil.assembleVariable(symbol)[0]
# check for a name space match
if symbol in name_spaces:
res_name = symbol
# see if symbol is a (dot-exact) prefix of any of class_names
else:
for class_name in class_names:
if (symbol.startswith(class_name) and
re.search(r'^%s(?=\.|$)' % re.escape(class_name), symbol)):
# e.g. re.search(r'^mylib.Foo(?=\.|$)', 'mylib.Foo.Bar' is
# true, but not with 'mylib.FooBar'
# take the longest match
if len(class_name) > len(res_name):
res_name = class_name
return res_name
|
class Solution:
def getLeastNumbers(self, arr: List[int], k: int) -> List[int]:
return heapq.nsmallest(k, arr)
|
from django.db import models
# Create your models here.
class Post(models.Model):
author = models.ForeignKey('auth.User')
title = models.CharField(max_length=256, default='')
text = models.TextField(default='')
creation_date = models.DateTimeField(blank=True, null=True)
def __str__(self):
return self.title |
from typing import TypedDict
class IConstituentConfig(TypedDict):
entity_tag: str
display_name: float
|
#! /usr/bin/env python3
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#
# Author: Giangi Sacco
# Copyright 2012, by the California Institute of Technology. ALL RIGHTS RESERVED. United States Government Sponsorship acknowledged.
#
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
import sys, traceback
from interferogram.insarMH import InsarMH
from utils.contextUtils import toContext
from interferogram.Interferogram import Interferogram
def createProject(inputs):
ifg = Interferogram()
ifg._project = inputs['project']
if(inputs['workflow'] == 'vanilla_isce'):
ifg._insarClass = InsarMH
return ifg
def main():
import json
inputs = json.load(open(sys.argv[1]))
'''Command line parsing.'''
'''
import argparse
parser = argparse.ArgumentParser(
description='Create an unwrapped tropospheric corrected interferogram in two stages.',
formatter_class=argparse.ArgumentDefaultsHelpFormatter
)
parser.add_argument('-i','--inputFile', action='store', default=None, dest='inputFile',
help='The json input file', type=str)
parser.add_argument('-s','--stage', action='store', default=0, dest='stage',
help='One of the two stage (0,1)', type=int)
parser.add_argument('-e','--errorCode', action='store', default=0, dest='errorCode',
help='The error code of the tropospheric correction step', type=int)
parser.add_argument('-p','--project', default='', dest='project',
help='project', type=str)
ops = parser.parse_args()
#ifg.createProductJson(ifg.createMetadata(filename))
'''
ifg = createProject(inputs)
ifg.run(inputs)
if __name__ == '__main__':
try: status = main()
except Exception as e:
with open('_alt_error.txt', 'w') as f:
f.write("%s\n" % str(e))
with open('_alt_traceback.txt', 'w') as f:
f.write("%s\n" % traceback.format_exc())
raise
sys.exit(status)
|
from ..grammar.state import Label, State, STATE_LABEL, States
from ..grammar.symbols import Symbols
from tokenize import NAME, OP, NEWLINE, ENDMARKER, ERRORTOKEN
class _Symbols(Symbols):
attr = 257
attrs = 258
item = 259
stmt = 260
module = 261
asdl = 262
symbols = _Symbols()
attr = State(False, 'attr', 257)
attrs = State(False, 'attrs', 258)
item = State(False, 'item', 259)
stmt = State(False, 'stmt', 260)
module = State(False, 'module', 261)
asdl = State(False, 'asdl', 262)
attr0 = attr
attr1 = State(False)
attr2 = State(False)
attr3 = State(True)
attr0.arc(Label(NAME), attr1)
attr1.arc(Label(OP, '*'), attr2)
attr1.arc(Label(ERRORTOKEN, '?'), attr2)
attr1.arc(Label(NAME), attr3)
attr2.arc(Label(NAME), attr3)
attrs0 = attrs
attrs1 = State(False)
attrs2 = State(False)
attrs3 = State(False)
attrs4 = State(True)
attrs0.arc(Label(OP, '('), attrs1)
attrs1.arc(Label(STATE_LABEL, attr), attrs2)
attrs2.arc(Label(OP, ','), attrs3)
attrs2.arc(Label(OP, ')'), attrs4)
attrs3.arc(Label(STATE_LABEL, attr), attrs2)
attrs3.arc(Label(NEWLINE), attrs3)
item0 = item
item1 = State(True)
item2 = State(True)
item0.arc(Label(NAME), item1)
item0.arc(Label(STATE_LABEL, attrs), item2)
item1.arc(Label(STATE_LABEL, attrs), item2)
stmt0 = stmt
stmt1 = State(False)
stmt2 = State(False)
stmt3 = State(True)
stmt4 = State(False)
stmt5 = State(True)
stmt0.arc(Label(NAME), stmt1)
stmt1.arc(Label(OP, '='), stmt2)
stmt2.arc(Label(STATE_LABEL, item), stmt3)
stmt3.arc(Label(NEWLINE), stmt3)
stmt3.arc(Label(OP, '|'), stmt2)
stmt3.arc(Label(NAME, 'attributes'), stmt4)
stmt4.arc(Label(STATE_LABEL, attrs), stmt5)
module0 = module
module1 = State(False)
module2 = State(False)
module3 = State(False)
module4 = State(True)
module0.arc(Label(NAME, 'module'), module1)
module1.arc(Label(NAME), module2)
module2.arc(Label(NEWLINE), module2)
module2.arc(Label(OP, '{'), module3)
module3.arc(Label(NEWLINE), module3)
module3.arc(Label(STATE_LABEL, stmt), module3)
module3.arc(Label(OP, '}'), module4)
asdl0 = asdl
asdl1 = State(False)
asdl2 = State(True)
asdl0.arc(Label(NEWLINE), asdl)
asdl0.arc(Label(STATE_LABEL, module), asdl1)
asdl1.arc(Label(NEWLINE), asdl1)
asdl1.arc(Label(ENDMARKER), asdl2)
states = {
'attr': attr,
'attrs': attrs,
'item': item,
'stmt': stmt,
'module': module,
'asdl': asdl,
}
states = States(**states)
states.build_bootstrap()
|
# -*- coding: utf-8 -*-
from multiprocessing import Pool
import math
import nltk
import sys
import os
def runn(data, index, size, path):
print("jjjjj"+str(index))
if __name__ == '__main__':
if len(sys.argv) == 2:
path = sys.argv[1]
f = open(path, "r", encoding='UTF-8')
print(path)
bline = f.readlines()
processor = 20
p = Pool(processor)
for i in range(processor):
p.apply_async(runn, args=(bline, i, processor, path), )
print("process "+str(i)+" is going on ~~")
p.close()
p.join()
f.close()
print("process ok~~")
else:
print("argv count error")
|
import numpy as np
import torch
from torch import nn
class LinearModel(nn.Module):
def __init__(self, dim_input, num_of_classes):
"""
Parameters
----------
dim_input: int > 0
number of neurons for this layer
num_of_classes: int > 0
number of classes
"""
super().__init__()
# number of input neurons
self.input_neurons = dim_input
# Layer
self.output = nn.Linear(dim_input, num_of_classes)
self.softmax = nn.Softmax()
def forward(self, x):
"""
Forward pass through the network
:param input: tabular data
:return: prediction
"""
output = self.output(x)
output = self.softmax(output)
# output = output.squeeze()
return output
def proba(self, data):
"""
Computes probabilistic output for two classes
:param data: torch tabular input
:return: np.array
"""
if not torch.is_tensor(data):
input = torch.from_numpy(np.array(data)).float()
# input = torch.squeeze(input)
else:
input = torch.squeeze(data)
class_1 = 1 - self.forward(input)
class_2 = self.forward(input)
return list(zip(class_1, class_2))
def prob_predict(self, data):
"""
Computes probabilistic output for two classes
:param data: torch tabular input
:return: np.array
"""
if not torch.is_tensor(data):
input = torch.from_numpy(np.array(data)).float()
# input = torch.squeeze(input)
else:
input = torch.squeeze(data)
class_1 = 1 - self.forward(input).detach().numpy().squeeze()
class_2 = self.forward(input).detach().numpy().squeeze()
# For single prob prediction it happens, that class_1 is casted into float after 1 - prediction
# Additionally class_1 and class_2 have to be at least shape 1
if not isinstance(class_1, np.ndarray):
class_1 = np.array(class_1).reshape(1)
class_2 = class_2.reshape(1)
return np.array(list(zip(class_1, class_2)))
def predict(self, data):
"""
predict method for CFE-Models which need this method.
:param data: torch or list
:return: np.array with prediction
"""
if not torch.is_tensor(data):
input = torch.from_numpy(np.array(data)).float()
# input = torch.squeeze(input)
else:
input = torch.squeeze(data)
return self.forward(input).detach().numpy()
|
import unittest
import tfexpt
import expt
class TestAccNative(unittest.TestCase):
def testIt(self):
acc,loss = expt.runMain(250)
self.assertTrue(acc >= 0.205)
class TestAccTF(unittest.TestCase):
def testIt(self):
acc = tfexpt.runMain(250)
self.assertTrue(acc >= 0.27)
if __name__ == "__main__":
unittest.main()
|
# This is an example VISAN script showing the extraction and plotting of ECMWF MARS data in GRIB format
# Make sure to set the 'products-file directory' option in the VISAN Preferences panel
# to a directory containing ECMWF MARS GRIB products.
# This example will then take the first product it finds in this directory and
# for that product plot the O3 column number density
def run():
import glob
import wx
productdir = str(wx.Config.Get().Read('DirectoryLocation/Products'))
# Use glob to find all files in productdir starting with 'C1D'
files = glob.glob(os.path.join(productdir, "*.grib"))
if len(files) == 0:
print(("Could not find any GRIB files in directory '" + productdir + "'"))
return
# We only take the first file
filename = files[0]
# O3 is by default provided as mass column densities
# During import we derive a new variable from this that contains a column number density with unit DU
# And at the end we remove the mass column density variable again since we don't need it anymore
data = harp.import_product(filename, "keep(latitude,longitude,O3_column_density);"
"derive(O3_column_number_density {latitude,longitude} [DU]);exclude(O3_column_density)")
wplot(data, colorrange=[150, 500])
run()
|
import json
import os
from builder.network_builder import Network
class Generator:
def __init__(self):
self.best_accuracy = 0
self.best_accuracy_logdir = None
self.best_network_spec = None
def get_best_spec (self, logdir):
# get all netswork.json
for subdir, dirs, files in os.walk(str(logdir)):
for file in files:
# filter
if file == 'network.json':
file_loc = os.path.join(subdir, file)
#read current network.json
with open(file_loc, 'r') as fp:
n_spec = json.loads( fp.read() )
if('results' in n_spec ):
if(self.best_accuracy < n_spec['results']['accuracy']):
self.best_accuracy = n_spec['results']['accuracy']
self.best_accuracy_logdir = file_loc
self.best_network_spec = n_spec
#self._write_to_logdir(logdir=logdir, n_spec=self.best_network_spec)
return self.best_network_spec
def _write_to_logdir(self, logdir, n_spec):
file_loc = os.path.join(logdir, 'Best_Network.json')
with open(file_loc, 'w') as fp:
fp.write(str(n_spec))
def main():
base_logdir = 'log'
output_logdir = base_logdir + '/best/'
generator = Generator()
json_network_spec = generator.get_best_spec(logdir = base_logdir)
print('best Network: ' + str(json_network_spec))
# workaround
json_network_spec['logdir'] = output_logdir
network = Network(json.dumps(json_network_spec))
network.evaluate(get_weights=True)
print('Finished')
main() |
import json
import glob
import io
data = {
"AUDIO": {
"SAMPLE_RATE": 8000,
"SPEAKERS_TRAINING_SET": [
],
"SPEAKERS_TESTING_SET": [
]
}
}
conf_jsonpath = '/home/rice/PycharmProjects/deep-speaker-master/conf.json'
speakerjson = data
train_speakerids = glob.glob('/run/media/rice/DATA/tripletdata_test/*')
B = len('/run/media/rice/DATA/tripletdata_test/')
print(train_speakerids)
for train_speaker in train_speakerids:
speakerjson["AUDIO"]["SPEAKERS_TESTING_SET"].append(train_speaker[B:])
test = json.dumps(speakerjson)
with io.open(conf_jsonpath, 'w', encoding='utf8') as outfile:
str_ = json.dumps(speakerjson,
indent=4, sort_keys=True,
separators=(',', ': '), ensure_ascii=False)
outfile.write(str_)
speakerjson = data
train_speakerids = glob.glob('/run/media/rice/DATA/TIMIT/*')
A = len('/run/media/rice/DATA/TIMIT/')
print(train_speakerids)
for train_speaker in train_speakerids:
speakerjson["AUDIO"]["SPEAKERS_TRAINING_SET"].append(train_speaker[A:])
test = json.dumps(speakerjson)
with io.open(conf_jsonpath, 'w', encoding='utf8') as outfile:
str_ = json.dumps(speakerjson,
indent=4, sort_keys=True,
separators=(',', ': '), ensure_ascii=False)
outfile.write(str_) |
import unittest
import zserio
from testutils import getZserioApi
class UnionTemplatedFieldTest(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.api = getZserioApi(__file__, "templates.zs").union_templated_field
def testReadWrite(self):
uintUnion = self.api.TemplatedUnion_uint16_uint32()
uintUnion.setField1(42)
floatUnion = self.api.TemplatedUnion_float32_float64()
floatUnion.setField2(4.2)
compoundUnion = self.api.TemplatedUnion_Compound_uint16_Compound_uint32()
compoundUnion.setField3(self.api.Compound_Compound_uint16.fromFields(
self.api.Compound_uint16.fromFields(13)
))
unionTemplatedField = self.api.UnionTemplatedField.fromFields(uintUnion, floatUnion, compoundUnion)
writer = zserio.BitStreamWriter()
unionTemplatedField.write(writer)
reader = zserio.BitStreamReader(writer.getByteArray())
readUnionTemplatedField = self.api.UnionTemplatedField()
readUnionTemplatedField.read(reader)
self.assertEqual(unionTemplatedField, readUnionTemplatedField)
|
plus = 'script/adblock+adguard.txt'
no = list(set(plus))
with open(plus,w) as f
f.write(no)
|
# -*- coding: utf-8 -*-
from pyquery import PyQuery
import datetime
import sqlite3
def delete_brands_generator():
url = 'http://www.jpx.co.jp/listing/stocks/delisted/index.html'
q = PyQuery(url)
for d, i in zip(q.find('tbody > tr > td:eq(0)'),
q.find('tbody > tr > td:eq(2)')):
date = datetime.datetime.strptime(d.text, '%Y/%m/%d').date()
yield (i.text, date)
def insert_delete_brands_to_db(db_file_name):
conn = sqlite3.connect(db_file_name)
with conn:
sql = 'INSERT INTO delete_brands(code,date) VALUES(?,?)'
conn.executemany(sql, delete_brands_generator())
|
# rps data for the rock-paper-scissors portion of the red-green game
# to be imported by rg.cgi
# this file represents the "host throw" for each numbered round
rps_data = {
0: "rock",
1: "rock",
2: "scissors",
3: "paper",
4: "paper",
5: "scissors",
6: "rock",
7: "scissors",
8: "paper",
9: "paper",
10: "scissors",
11: "rock",
12: "paper",
13: "paper",
14: "rock",
15: "scissors",
16: "scissors",
17: "scissors",
18: "rock",
19: "scissors",
20: "paper",
21: "rock",
22: "paper",
23: "scissors",
24: "rock",
25: "scissors",
26: "rock",
27: "rock",
28: "paper",
29: "paper",
30: "rock",
31: "paper",
32: "paper",
33: "scissors",
34: "rock",
35: "rock",
36: "scissors",
37: "rock",
38: "rock",
39: "paper",
40: "rock",
41: "rock",
42: "paper",
43: "paper",
44: "paper",
45: "paper",
46: "scissors",
47: "rock",
48: "scissors",
49: "scissors",
}
|
# Generated by Django 3.0.3 on 2020-04-17 21:18
from django.db import migrations, models
class Migration(migrations.Migration):
dependencies = [
('usermanagement', '0008_profile_anonymous'),
]
operations = [
migrations.AlterField(
model_name='profile',
name='NTNUI_medlem',
field=models.BooleanField(default=False, verbose_name='Jeg er NTNUI-medlem'),
),
migrations.AlterField(
model_name='profile',
name='anonymous',
field=models.BooleanField(default=True, verbose_name='Jeg ønsker å være anonym overfor andre brukere på siden'),
),
]
|
import data.model
from endpoints.keyserver.models_interface import (
KeyServerDataInterface,
ServiceKey,
ServiceKeyDoesNotExist,
)
class PreOCIModel(KeyServerDataInterface):
"""
PreOCIModel implements the data model for JWT key service using a database schema before it was
changed to support the OCI specification.
"""
def list_service_keys(self, service):
return data.model.service_keys.list_service_keys(service)
def get_service_key(self, signer_kid, service=None, alive_only=True, approved_only=True):
try:
key = data.model.service_keys.get_service_key(
signer_kid, service, alive_only, approved_only
)
return _db_key_to_servicekey(key)
except data.model.ServiceKeyDoesNotExist:
raise ServiceKeyDoesNotExist()
def create_service_key(
self, name, kid, service, jwk, metadata, expiration_date, rotation_duration=None
):
key = data.model.service_keys.create_service_key(
name, kid, service, jwk, metadata, expiration_date, rotation_duration
)
return _db_key_to_servicekey(key)
def replace_service_key(self, old_kid, kid, jwk, metadata, expiration_date):
try:
data.model.service_keys.replace_service_key(
old_kid, kid, jwk, metadata, expiration_date
)
except data.model.ServiceKeyDoesNotExist:
raise ServiceKeyDoesNotExist()
def delete_service_key(self, kid):
try:
key = data.model.service_keys.delete_service_key(kid)
return _db_key_to_servicekey(key)
except data.model.ServiceKeyDoesNotExist:
raise ServiceKeyDoesNotExist()
pre_oci_model = PreOCIModel()
def _db_key_to_servicekey(key):
"""
Converts the Pre-OCI database model of a service key into a ServiceKey.
"""
return ServiceKey(
name=key.name,
kid=key.kid,
service=key.service,
jwk=key.jwk,
metadata=key.metadata,
created_date=key.created_date,
expiration_date=key.expiration_date,
rotation_duration=key.rotation_duration,
approval=key.approval,
)
|
from distutils.core import setup
long_description = """
A pure-Python tiling window manager.
Features
========
* Simple, small and extensible. It's easy to write your own layouts,
widgets and commands.
* Configured in Python.
* Command shell that allows all aspects of
Qtile to be managed and inspected.
* Complete remote scriptability - write scripts to set up workspaces,
manipulate windows, update status bar widgets and more.
* Qtile's remote scriptability makes it one of the most thoroughly
unit-tested window mangers around.
Qtile depends on the Python X Library (http://python-xlib.sourceforge.net/).
"""
"""
The content below is included from the distextend project.
The code is in the public domain, and may be used for any purpose
whatsoever.
"""
import fnmatch
import os.path
def _fnmatch(name, patternList):
for i in patternList:
if fnmatch.fnmatch(name, i):
return True
return False
def _splitAll(path):
parts = []
h = path
while 1:
if not h:
break
h, t = os.path.split(h)
parts.append(t)
parts.reverse()
return parts
def findPackages(path, dataExclude=[]):
"""
Recursively find all packages and data directories rooted at path. Note
that only data _directories_ and their contents are returned -
non-Python files at module scope are not, and should be manually
included.
dataExclude is a list of fnmatch-compatible expressions for files and
directories that should not be included in pakcage_data.
Returns a (packages, package_data) tuple, ready to be passed to the
corresponding distutils.core.setup arguments.
"""
packages = []
datadirs = []
for root, dirs, files in os.walk(path, topdown=True):
if "__init__.py" in files:
p = _splitAll(root)
packages.append(".".join(p))
else:
dirs[:] = []
if packages:
datadirs.append(root)
package_data = {}
for i in datadirs:
if not _fnmatch(i, dataExclude):
parts = _splitAll(i)
module = ".".join(parts[:-1])
acc = package_data.get(module, [])
for root, dirs, files in os.walk(i, topdown=True):
sub = os.path.join(*_splitAll(root)[1:])
if not _fnmatch(sub, dataExclude):
for fname in files:
path = os.path.join(sub, fname)
if not _fnmatch(path, dataExclude):
acc.append(path)
else:
dirs[:] = []
package_data[module] = acc
return packages, package_data
packages, package_data = findPackages("libqtile")
setup(
name="qtile",
version="0.5",
description="A pure-Python tiling window manager.",
author="Aldo Cortesi",
author_email="aldo@nullcube.com",
license="MIT",
url="http://www.qtile.org",
packages=packages,
package_data=package_data,
scripts=["qtile-session", "qtile", "qsh"],
classifiers=[
"Intended Audience :: End Users/Desktop",
"License :: OSI Approved :: MIT License",
"Development Status :: 3 - Alpha",
"Programming Language :: Python",
"Operating System :: Unix",
"Topic :: Desktop Environment :: Window Managers",
]
)
|
# -*- coding: utf-8 -*-
"""
Created on Fri Oct 2 11:03:28 2020
@author: Tarun Jaiswal
"""
a=int(input("Enter the first no="))
b=int(input("Enter the second no= "))
c=int(input("Enter the third no="))
print("a={0}".format(a))
print("b={0}".format(b))
print("c={0}".format(c))
if a>=b and a>=c:
max=a
else:
if b>=c:
max=b
else:
max=c
print(max) |
# -*- coding: utf-8 -*-
"""
Batch sampler
Defines how to sample the streamlines available in the MultiSubjectData.
- Defines the __iter__ method:
- Finds a list of streamlines ids and associated subj that you can later
load in your favorite way.
- It is possible to restrict the number of subjects in a batch (and thus
the number of inputs to load associated with sampled streamlines), and to
reduce the number of time we need to load new data by using the same
subjects for a given number of "cycles".
USAGE:
Can be used in a torch DataLoader. For instance:
# Initialize dataset
dataset = MultiSubjectDataset(...)
dataset.load_training_data()
# Initialize batch sampler
batch_sampler = BatchSampler(...)
# Use this in the dataloader
dataloader = DataLoader(dataset, batch_sampler=batch_sampler,
collate_fn=batch_loader.load_batch)
"""
import logging
from typing import List, Tuple, Iterator
import numpy as np
import torch
import torch.multiprocessing
from torch.utils.data import Sampler
from dwi_ml.experiment_utils.prints import TqdmLoggingHandler
from dwi_ml.data.dataset.multi_subject_containers import MultisubjectSubset
class DWIMLBatchSampler(Sampler):
def __init__(self, dataset: MultisubjectSubset,
streamline_group_name: str, batch_size: int,
batch_size_units: str, nb_streamlines_per_chunk: int,
rng: int, nb_subjects_per_batch: int, cycles: int):
"""
Parameters
----------
dataset : MultisubjectSubset
Dataset to sample from.
streamline_group_name: str
The name of the group to use to load the sequences among all
streamline_groups in the data_source.
batch_size : int
Batch size. Can be defined in number of streamlines or in total
length_mm (specified through batch_size_units).
batch_size_units: str
'nb_streamlines' or 'length_mm' (which should hopefully be
correlated to the number of input data points).
nb_streamlines_per_chunk: int
In the case of a batch size in terms of 'length_mm', chunks of n
streamlines are sampled at once, and then their size is checked,
either removing streamlines if exceeded, or else sampling a new
chunk of ids.
rng : int
Seed for the random number generator.
nb_subjects_per_batch : int
Maximum number of subjects to be used in a single batch. Depending
on the model, this can avoid loading too many input volumes at the
same time, for example. If None, always sample from all subjects.
cycles : int
Used if `nb_subjects_per_batch` is given. Number of batches
re-using the same subjects (and thus the same volumes) before
sampling new ones.
"""
super().__init__(dataset) # This does nothing but python likes it.
# Checking that batch_size is correct
if not isinstance(batch_size, int) or batch_size <= 0:
raise ValueError("batch_size (i.e. number of total timesteps in "
"the batch) should be a positive integeral "
"value, but got batch_size={}"
.format(batch_size))
if batch_size_units not in ['nb_streamlines', 'length_mm']:
raise ValueError("batch_size_unit should either be "
"'nb_streamlines' or 'length_mm'")
if (batch_size_units == 'nb_streamlines' and
nb_streamlines_per_chunk != batch_size):
logging.warning("With a max_batch_size computed in terms of "
"number of streamlines, the chunk size is not "
"used. Ignored")
# Checking that n_volumes was given if cycles was given
if cycles and not nb_subjects_per_batch:
raise ValueError("If `cycles` is defined, "
"`nb_subjects_per_batch` should be defined. Got: "
"nb_subjects_per_batch={}, cycles={}"
.format(nb_subjects_per_batch, cycles))
# Batch sampler variables
self.dataset = dataset
self.streamline_group_name = streamline_group_name
self.nb_subjects_per_batch = nb_subjects_per_batch
self.cycles = cycles
if batch_size_units == 'nb_streamlines':
self.nb_streamlines_per_chunk = batch_size
else:
self.nb_streamlines_per_chunk = nb_streamlines_per_chunk
self.batch_size = batch_size
self.batch_size_units = batch_size_units
# Find idx of streamline group
self.streamline_group_idx = self.dataset.streamline_groups.index(
self.streamline_group_name)
# Set random numbers
self.rng = rng
self.np_rng = np.random.RandomState(self.rng)
torch.manual_seed(self.rng) # Set torch seed
# Batch sampler's logging level can be changed separately from main
# scripts.
self.logger = logging.getLogger('batch_sampler_logger')
self.logger.propagate = False
self.logger.setLevel(logging.root.level)
def make_logger_tqdm_fitted(self):
"""Possibility to use a tqdm-compatible logger in case the model
is used through a tqdm progress bar."""
self.logger.addHandler(TqdmLoggingHandler())
@property
def params(self):
"""
All parameters. Contains at least all parameters that would be
necessary to create this batch sampler again (except the dataset).
"""
params = {
'streamline_group_name': self.streamline_group_name,
'batch_size': self.batch_size,
'batch_size_units': self.batch_size_units,
'nb_streamlines_per_chunk': self.nb_streamlines_per_chunk,
'rng': self.rng,
'nb_subjects_per_batch': self.nb_subjects_per_batch,
'cycles': self.cycles,
'type': type(self),
}
return params
@property
def states(self):
states = {
'rng_state': self.np_rng.get_state(),
}
return states
def __iter__(self) -> Iterator[List[Tuple[int, list]]]:
"""
Streamline sampling.
First sample the subjects to be used from a given number of desired
subjects, then sample streamline ids inside those volumes.
Hint: To use this through the dataload, through a tqdm progress bar:
with tqdm(dataloader) as pbar:
train_iterator = enumerate(pbar)
for batch_id, data in train_iterator:
...
Returns
-------
batch_ids_per_subj : list[(int, list)]
- The torch's dataloader will get this list and iterate on it, each
time using __iter__ function of the dataset (a multisubjectSubset)
to create a data and send it to the collate_fn (our load_batch).
- This must be a list.
- Inside the tuple, the int is the subject id and the list is
the list of streamlines ids for this subject.
- The list of streamline ids are relative ids inside each subject's
tractogram).
"""
# This is the list of all possible streamline ids
global_streamlines_ids = np.arange(
self.dataset.total_nb_streamlines[self.streamline_group_idx])
ids_per_subjs = \
self.dataset.streamline_ids_per_subj[self.streamline_group_idx]
# This contains one bool per streamline:
# 1 = this streamline has not been used yet.
# 0 = this streamline has been used.
global_unused_streamlines = np.ones_like(global_streamlines_ids)
self.logger.debug("********* Entering batch sampler iteration!\n"
" Choosing out of {} possible streamlines"
.format(sum(global_unused_streamlines)))
# This will continue "yielding" batches until it encounters a break.
# (i.e. when all streamlines have been used)
while True:
# Weight subjects by their number of remaining streamlines
streamlines_per_subj = np.array(
[np.sum(global_unused_streamlines[subj_id_slice])
for _, subj_id_slice in ids_per_subjs.items()])
assert (np.sum(streamlines_per_subj) ==
np.sum(global_unused_streamlines)), \
"Unexpected error, the total number of streamlines per " \
"subject does not correspond to the total number of " \
"streamlines in the multisubject dataset. Error in " \
"streamline ids?"
# Stopping if all streamlines have been used
if np.sum(streamlines_per_subj) == 0:
self.logger.info("No streamlines remain for this epoch, "
"stopping...")
break
# Choose subjects from which to sample streamlines for the next
# few cycles.
if self.nb_subjects_per_batch:
# Sampling first from subjects that were not seed a lot yet
weights = streamlines_per_subj / np.sum(streamlines_per_subj)
# Choosing only non-empty subjects
nb_subjects = min(self.nb_subjects_per_batch,
np.count_nonzero(weights))
sampled_subjs = self.np_rng.choice(
np.arange(len(self.dataset.subjs_data_list)),
size=nb_subjects, replace=False, p=weights)
else:
# Sampling from all subjects
sampled_subjs = ids_per_subjs.keys()
nb_subjects = len(sampled_subjs)
self.logger.debug(' Sampled subjects for the next few cycles: '
'{}'.format(sampled_subjs))
# Final subject's batch size could be smaller if no streamlines are
# left for this subject.
max_batch_size_per_subj = self.batch_size / nb_subjects
# Preparing to iterate on these chosen subjects for a predefined
# number of cycles
if self.cycles:
iterator = range(self.cycles)
else:
# Infinite iterator, sampling from all subjects
iterator = iter(int, 1)
count_cycles = 0
for _ in iterator:
count_cycles += 1
self.logger.debug(
" Iteration for cycle # {}/{}."
.format(count_cycles,
self.cycles if self.cycles else 'inf'))
batch_ids_per_subj = []
for subj in sampled_subjs:
sampled_ids = self._sample_streamlines_for_subj(
subj, ids_per_subjs, global_unused_streamlines,
max_batch_size_per_subj)
# Append tuple (subj, list_sampled_ids) to the batch
batch_ids_per_subj.append((subj, sampled_ids))
self.logger.debug(
" Finished loop on subjects. Now yielding.\n"
" (If this was called through a dataloader, it should "
"start using load_batch and even training \n"
" on this batch while we prepare a batch for the next "
"cycle, if any).")
if len(batch_ids_per_subj) == 0:
self.logger.debug(
"No more streamlines remain in any of the selected "
"volumes! Breaking now. You may call the next "
"iteration of this batch sampler!")
break
yield batch_ids_per_subj
# Finished cycle. Will choose new subjs if the number of iterations
# is not reached for this __iter__ call.
def _sample_streamlines_for_subj(self, subj, ids_per_subjs,
global_unused_streamlines,
max_batch_size_per_subj):
"""
For each subject, randomly choose streamlines that have not been chosen
yet.
Params:
------
subj: int
The subject's id.
ids_per_subjs: dict
The list of this subject's streamlines' global ids.
global_unused_streamlines: array
One flag per global streamline id: 0 if already used, else 1.
max_batch_size_per_subj:
Max batch size to load for this subject.
"""
sampled_ids = []
# Get the global streamline ids corresponding to this
# subject
subj_slice = ids_per_subjs[subj]
# We will continue iterating on this subject until we
# break (i.e. when we reach the maximum batch size for this
# subject)
total_subj_batch_size = 0
while True:
# Add some more streamlines for this subject.
(subbatch_global_ids, subbatch_rel_ids,
subj_subbatch_size,
no_streamlines_left, reached_max) = \
self._get_a_chunk_of_streamlines(
subj_slice, global_unused_streamlines,
total_subj_batch_size, max_batch_size_per_subj)
if no_streamlines_left:
# No streamlines remaining. Get next subject.
break
if len(subbatch_rel_ids) == 0:
logging.warning(
"MAJOR WARNING. Got no streamline for this subject in "
"this batch, but there are streamlines left. \n"
"Possibly means that the allowed batch size does not even "
"allow one streamline per batch.\n Check your batch size "
"choice!")
# Mask the sampled streamlines
global_unused_streamlines[subbatch_global_ids] = 0
# Add sub-sampled ids to subject's batch
sampled_ids.extend(subbatch_rel_ids)
# Continue?
if reached_max:
# Batch size reached for this subject. Get next subject.
break
else:
# Update size and get a new chunk
total_subj_batch_size += subj_subbatch_size
return sampled_ids
def _get_a_chunk_of_streamlines(self, subj_slice,
global_unused_streamlines,
current_subbatch_size, max_subbatch_size):
"""
Get a chunk of streamlines (for a given subject) and evaluate their
size.
Params
------
subj_slice: slice
All global streamline ids belonging to a given subject.
global_unused_streamlines: array
One flag per global streamline id: 0 if already used, else 1.
current_subbatch_size: int
Chunks's size + current_subbatch_size must not exceed
max_subbatch_size.
max_subbatch_size: int
Maximum batch size for current subject.
Returns:
chosen_global_ids: list
The list of global ids chosen for this chunk
chosen_relative_ids:
The same ids, but in terms of relative ids for current subject.
no_streamlines_remaining: bool
If true, all of this subject's streamlines have been used.
reached_max_heaviness)
"""
no_streamlines_remaining = False
reached_max_heaviness = False
# Find streamlines that have not been used yet for this subj
subj_unused_ids_in_global = np.flatnonzero(
global_unused_streamlines[subj_slice]) + subj_slice.start
self.logger.debug(" Available streamlines for this subject: {}"
.format(len(subj_unused_ids_in_global)))
# No streamlines remain for this subject
if len(subj_unused_ids_in_global) == 0:
no_streamlines_remaining = True
return [], [], no_streamlines_remaining, reached_max_heaviness
# Sample a chunk of streamlines
chosen_global_ids = self.np_rng.choice(subj_unused_ids_in_global,
self.nb_streamlines_per_chunk)
# Compute chunk size and remove streamlines from it if necessary
size_per_streamline = self._compute_and_adjust_batch_size(
chosen_global_ids)
# If batch_size has been exceeded, taking a little less streamlines
# for this chunk.
computed_chunk_size = np.sum(size_per_streamline)
if current_subbatch_size + computed_chunk_size >= max_subbatch_size:
cumulative_sum = np.cumsum(size_per_streamline)
selected = cumulative_sum < (max_subbatch_size -
current_subbatch_size)
chosen_global_ids = chosen_global_ids[selected]
size_per_streamline = size_per_streamline[selected]
reached_max_heaviness = True
computed_chunk_size = np.sum(size_per_streamline)
self.logger.debug(
" Chunk_size was {} streamlines, but after verifying data "
"(max batch size for this subj is {}), keeping only {} "
"streamlines for a total of {} (units = {})."
.format(self.nb_streamlines_per_chunk, max_subbatch_size,
len(chosen_global_ids), computed_chunk_size,
self.batch_size_units))
# Fetch subject-relative ids
chosen_relative_ids = list(chosen_global_ids - subj_slice.start)
return (chosen_global_ids, chosen_relative_ids, computed_chunk_size,
no_streamlines_remaining, reached_max_heaviness)
def _compute_and_adjust_batch_size(self, chosen_global_ids):
"""
Relying on the lengths_mm info available in the MultiSubjectData to be
able to know the (eventual, if self.step_size) number of time steps
without loading the streamlines, particularly with the lazy data.
"""
if self.batch_size_units == 'length_mm':
l_mm = self.dataset.streamline_lengths_mm
l_mm = l_mm[self.streamline_group_idx][chosen_global_ids]
size_per_streamline = l_mm
else: # units = nb_streamlines
size_per_streamline = np.ones(len(chosen_global_ids))
return size_per_streamline
|
import os
import unittest
from unittest.mock import patch
from requests.auth import HTTPBasicAuth
from shutterstock.utils.prettyprint import pretty_print
from shutterstock.utils.request import get, put, post, delete
from shutterstock.utils.request_helper import RequestHelper
class UtilTests(unittest.TestCase):
"""
CLI Utility Tests
"""
def test_pretty_print(self):
"""
Tests pretty print function.
"""
data = {"a": 1, "b": 2}
self.assertLogs(pretty_print(data))
class RequestHelperTests(unittest.TestCase):
"""
Request Helper Tests.
"""
def setUp(self) -> None:
self.key = "SHUTTERSTOCK_KEY"
self.secret = "SHUTTERSTOCK_SECRET"
self.token = "SHUTTERSTOCK_API_TOKEN"
self.sandbox_mode = "SHUTTERSTOCK_SANDBOX"
self.custom_url = "SHUTTERSTOCK_CUSTOM_URL"
if self.key in os.environ:
del os.environ[self.key]
if self.secret in os.environ:
del os.environ[self.secret]
if self.token in os.environ:
del os.environ[self.token]
if self.sandbox_mode in os.environ:
del os.environ[self.sandbox_mode]
if self.custom_url in os.environ:
del os.environ[self.custom_url]
def test_request_helper_with_token(self):
"""
Asserts we can set up header auth correctly.
"""
os.environ[self.token] = "1"
req = RequestHelper()
self.assertEqual(req.headers, {"Authorization": "Bearer 1"})
self.assertIsNone(req.auth)
def test_request_helper_with_auth(self):
"""
Asserts we can set up basic auth correctly.
"""
os.environ[self.key] = "a"
os.environ[self.secret] = "b"
req = RequestHelper()
self.assertIsInstance(req.auth, HTTPBasicAuth)
self.assertEqual(req.headers, {})
def test_request_helper_base_url(self):
"""
Asserts we can set the base endpoint.
"""
os.environ[self.sandbox_mode] = "true"
req = RequestHelper()
self.assertEqual(req.base_endpoint, "https://api-sandbox.shutterstock.com")
class RequestTests(unittest.TestCase):
"""
Request Tests
"""
def setUp(self) -> None:
os.environ["SHUTTERSTOCK_API_TOKEN"] = "a"
self.headers = {"Authorization": "Bearer a"}
self.response_data = {"a": 1, "b": 2}
self.base_endpoint = "https://api.shutterstock.com"
@patch("requests.get")
def test_get(self, mock_get):
"""
Asserts we are calling the GET function properly.
"""
mock_get.return_value.json.return_value = self.response_data
url = "/v2/images/search"
params = {"query": "poland"}
get(url, params)
mock_get.assert_called_with(
url=f"{self.base_endpoint}{url}",
params=params,
headers=self.headers,
auth=None,
)
self.assertLogs(pretty_print(self.response_data))
@patch("requests.post")
def test_post(self, mock_post):
"""
Asserts we are calling the POST function properly.
"""
mock_post.return_value.json.return_value = self.response_data
url = "/v2/images/search"
params = {"query": "poland"}
data = {"a": 1, "b": 2}
post(url, params, data)
mock_post.assert_called_with(
url=f"{self.base_endpoint}{url}",
json=data,
params=params,
headers=self.headers,
auth=None,
)
self.assertLogs(pretty_print(self.response_data))
@patch("requests.put")
def test_put(self, mock_put):
"""
Asserts we are calling the PUT function properly.
"""
mock_put.return_value.json.return_value = self.response_data
url = "/v2/images/search"
params = {"query": "poland"}
data = {"a": 1, "b": 2}
put(url, params, data)
mock_put.assert_called_with(
url=f"{self.base_endpoint}{url}",
params=params,
json=data,
headers=self.headers,
auth=None,
)
self.assertLogs(pretty_print(self.response_data))
@patch("requests.delete")
def test_delete(self, mock_delete):
"""
Asserts we are calling the DELETE function properly.
"""
mock_delete.return_value.json.return_value = self.response_data
url = "/v2/images/search"
params = {"query": "poland"}
data = {"a": 1, "b": 2}
delete(url, params, data)
mock_delete.assert_called_with(
url=f"{self.base_endpoint}{url}",
params=params,
json=data,
headers=self.headers,
auth=None,
)
self.assertLogs(pretty_print(self.response_data))
|
from django.forms import ModelForm ,Textarea
from reports.models import DailyReport ,ReportActivity
from django import forms
class ReportActivityForm(ModelForm):
class Meta:
model=ReportActivity
fields=['activity','cp','area','description','remarks']
# widgets={
# 'description':Textarea(attrs={'cols':100 ,'rows':3 }),
# 'remarks':Textarea(attrs={'cols':100 ,'rows':3}),
# }
# def __init__(self,*args, **kwargs):
# super().__init__(*args, **kwargs)
# self.fields['description'].widget.attrs.update({'class':'description'})
class DailyReportForm(ModelForm):
class Meta:
model=DailyReport
fields='__all__'
|
import torch
import torch.nn as nn
import torch.nn.functional as F
from chk import checkpoint_sequential_step, checkpoint
import math
import numpy as np
from torchvision.utils import save_image
import gin
def ginM(n): return gin.query_parameter(f'%{n}')
gin.external_configurable(nn.MaxPool2d, module='nn')
gin.external_configurable(nn.Upsample, module='nn')
class LN(nn.Module):
def forward(self, x):
return F.layer_norm(x, x.size()[1:], weight=None, bias=None, eps=1e-05)
@gin.configurable
class PadPool(nn.Module):
def forward(self, x):
x = F.pad(x, [0, 0, 0, 1])
x = F.max_pool2d(x,(2, 2), stride=(1, 2))
return x
def pCnv(inp,out,groups=1):
return nn.Sequential(
nn.Conv2d(inp,out,1,bias=False,groups=groups),
nn.InstanceNorm2d(out,affine=True)
)
#regarding same padding in PT https://github.com/pytorch/pytorch/issues/3867
def dsCnv(inp,k):
return nn.Sequential(
nn.Conv2d(inp,inp,k,groups=inp,bias=False,padding=(k - 1) // 2),
nn.InstanceNorm2d(inp,affine=True)
)
ngates = 2
class Gate(nn.Module):
def __init__(self,ifsz):
super().__init__()
self.ln = LN()
def forward(self, x):
t0,t1 = torch.chunk(x, ngates, dim=1)
t0 = torch.tanh_(t0)
t1.sub_(2)
t1 = torch.sigmoid_(t1)
return t1*t0
def customGC(module):
def custom_forward(*inputs):
inputs = module(inputs[0])
return inputs
return custom_forward
@gin.configurable
class GateBlock(nn.Module):
def __init__(self, ifsz, ofsz, gt = True, ksz = 3, GradCheck=gin.REQUIRED):
super().__init__()
cfsz = int( math.floor(ifsz/2) )
ifsz2 = ifsz + ifsz%2
self.sq = nn.Sequential(
pCnv(ifsz, cfsz),
dsCnv(cfsz,ksz),
nn.ELU(),
###########
pCnv(cfsz, cfsz*ngates),
dsCnv(cfsz*ngates,ksz),
Gate(cfsz),
###########
pCnv(cfsz, ifsz),
dsCnv(ifsz,ksz),
nn.ELU(),
)
self.gt = gt
self.gc = GradCheck
def forward(self, x):
if self.gc >= 1:
y = checkpoint(customGC(self.sq), x)
else:
y = self.sq(x)
out = x + y
return out
@gin.configurable
class InitBlock(nn.Module):
def __init__(self, fup, n_channels):
super().__init__()
self.n1 = LN()
self.Initsq = nn.Sequential(
pCnv(n_channels, fup),
nn.Softmax(dim=1),
dsCnv(fup,11),
LN()
)
def forward(self, x):
x = self.n1(x)
xt = x
x = self.Initsq(x)
x = torch.cat([x,xt],1)
return x
@gin.configurable
class OrigamiNet(nn.Module):
def __init__(self, n_channels, o_classes, wmul, lreszs, lszs, nlyrs, fup, GradCheck, reduceAxis=3):
super().__init__()
self.lreszs = lreszs
self.Initsq = InitBlock(fup)
layers = []
isz = fup + n_channels
osz = isz
for i in range(nlyrs):
osz = int( math.floor(lszs[i] * wmul) ) if i in lszs else isz
layers.append( GateBlock(isz, osz, True, 3) )
if isz != osz:
layers.append( pCnv(isz, osz) )
layers.append( nn.ELU() )
isz = osz
if i in lreszs:
layers.append( lreszs[i] )
layers.append( LN() )
self.Gatesq = nn.Sequential(*layers)
self.Finsq = nn.Sequential(
pCnv(osz, o_classes),
nn.ELU(),
)
self.n1 = LN()
self.it=0
self.gc = GradCheck
self.reduceAxis = reduceAxis
def forward(self, x, t=[]):
x = self.Initsq(x)
if self.gc >=2:
x = checkpoint_sequential_step(self.Gatesq,4,x) #slower, more memory save
# x = checkpoint_sequential_step(self.Gatesq,8,x) #faster, less memory save
else:
x = self.Gatesq(x)
x = self.Finsq(x)
x = torch.mean(x, self.reduceAxis, keepdim=False)
x = self.n1(x)
x = x.permute(0,2,1)
return x |
# encoding: utf-8
# Author: Bingxin Ke
# Created: 2021/10/28
from collections import defaultdict
from src.io import RasterReader, RasterWriter
from src.utils.libraster import dilate_mask
import numpy as np
import os
from typing import Dict
from rasterio.transform import Affine
from tabulate import tabulate
from datetime import datetime
DEFAULT_VALUE = -9999
class DSMEvaluator:
def __init__(self, gt_dsm_path: str, gt_mask_path: str = None, other_mask_path_dict: Dict[str, str] = None):
# self.gt_dsm: np.ndarray = gt_dsm
self._gt_dsm_reader = RasterReader(gt_dsm_path)
self.gt_dsm = self._gt_dsm_reader.get_data()
# load gt mask
if gt_mask_path is not None:
self._gt_mask_reader = RasterReader(gt_mask_path)
self.gt_mask = self._gt_mask_reader.get_data().astype(np.bool)
else:
self.gt_mask = np.ones(self.gt_dsm.shape)
# load other masks
if len(other_mask_path_dict) > 0:
self.other_mask: Dict[str, np.ndarray] = {key: RasterReader(path).get_data().astype(np.bool)
for key, path in other_mask_path_dict.items()}
if 'building' in self.other_mask.keys():
# dilate building mask by 2 pixels
self.other_mask['building'] = dilate_mask(self.other_mask['building'], iterations=2)
# terrain
self.other_mask['terrain'] = ~self.other_mask['building']
if 'water' in self.other_mask.keys():
self.other_mask['terrain_wo_water'] = self.other_mask['terrain'] & ~self.other_mask['water']
if 'forest' in self.other_mask.keys():
self.other_mask['terrain_wo_forest'] = self.other_mask['terrain'] & ~self.other_mask['forest']
else:
self.other_mask = None
def eval(self, target_dsm: np.ndarray, T: Affine, save_to: str = None):
# gt_dsm = self.gt_dsm
target_shape = target_dsm.shape
# T_inv = ~T
# clip gt dsm and masks
tl_bound = T * np.array([0, 0])
# br_bound = T * np.array([target_shape[1], target_shape[0]])
# _edge_length = (np.array(br_bound) - np.array(tl_bound)) * np.array([1, -1])
# area = _edge_length[0] * _edge_length[1]
l_col, t_row = np.floor(self._gt_dsm_reader.T_inv * tl_bound).astype(int)
gt_dsm_clip_arr = self.gt_dsm[t_row:t_row + target_shape[0], l_col:l_col + target_shape[1]]
gt_mask_clip_arr = self.gt_mask[t_row:t_row + target_shape[0], l_col:l_col + target_shape[1]]
# print(np.where(np.isnan(target_dsm) == True))
# print('gt_mask_clip_arr', gt_mask_clip_arr)
# print(gt_dsm_clip_arr.shape)
# print(gt_dsm_clip_arr[gt_mask_clip_arr].shape)
# original residual
residuals_arr = target_dsm - gt_dsm_clip_arr
# output_dic statistics
output_statistics = defaultdict()
# Overall residual
# apply gt mask
residuals_arr_gt = residuals_arr[gt_mask_clip_arr]
# remove nan values
residuals_arr_gt = residuals_arr_gt[np.where(np.isnan(residuals_arr_gt) == False)]
# statistics
_statistics = self.calculate_statistics(residuals_arr_gt)
output_statistics['overall'] = _statistics
# Different land types
if self.other_mask is not None:
for land_type, mask in self.other_mask.items():
# clip mask
_mask_clip = mask[t_row:t_row + target_shape[0], l_col:l_col + target_shape[1]]
# operation 'and' with gt mask
gt_land_mask = gt_mask_clip_arr & _mask_clip
masked_residual = residuals_arr[gt_land_mask]
# remove nan values
masked_residual = masked_residual[np.where(np.isnan(masked_residual) == False)]
_statistics = self.calculate_statistics(masked_residual)
output_statistics[land_type] = _statistics
# Residual dsm
diff_arr = residuals_arr * gt_mask_clip_arr
diff_arr[~gt_mask_clip_arr] = np.nan
return output_statistics, diff_arr
@staticmethod
def calculate_statistics(residual: np.ndarray):
if residual.shape[0] > 0:
residual_abs = np.abs(residual)
output_dic = defaultdict(float)
output_dic['max'] = np.max(residual)
output_dic['min'] = np.min(residual)
output_dic['MAE'] = np.mean(residual_abs) # mean absolute error
output_dic['RMSE'] = np.sqrt(np.mean(residual**2))
output_dic['abs_median'] = np.median(residual_abs)
output_dic['median'] = np.median(residual)
output_dic['n_pixel'] = residual.size
# Normalized median absolute deviation
output_dic['NMAD'] = 1.4826 * np.median(np.abs(residual - output_dic['abs_median']))
else:
output_dic = {'max': None, 'min': None, 'MAE': None, 'RMSE': None, 'abs_median': None, 'median': None, 'n_pixel': None, 'NMAD': None}
return output_dic
def print_statistics(statistic_dic: Dict, title: str, save_to: str = None, include_time=True):
head_line_keys = { # head line: statistics keys
'MAE[m]': 'MAE',
'RMSE[m]': 'RMSE',
'MedAE[m]': 'abs_median',
'Max[m]': 'max',
'Min[m]': 'min',
'Median[m]': 'median',
'NMAD[m]': 'NMAD',
'#Pixels': 'n_pixel'
}
output_str = "DSM Evaluation"
output_str += '\t' * 3 + 'created: ' + datetime.now().strftime('%Y-%m-%d %H:%M:%S') + '\n\n'
# title
output_str += title + '\n\n'
output_str += "Performance Evaluation \n"
output_str += "=" * 20 + '\n'
# Table
head_line = list(head_line_keys.keys())
content = []
for mask_type, dic in statistic_dic.items():
line = [mask_type.capitalize()]
for metric in head_line:
key = head_line_keys[metric]
line.append(dic[key])
content.append(line)
head_line.insert(0, 'Type')
output_str += tabulate(content, headers=head_line, tablefmt="simple", floatfmt=".4f") + '\n'
# Description
output_str += '-' * 20 + '\n'
output_str += """ Metrics:
MAE: Mean Absolute residual Error
RMSE: Root Mean Square Error
MedAE: Median Absolute Error
Max: Maximum value
Min: Minimum value
Median: Median value
NMAD: Normalised Median Absolute Deviation
#pixels: Number of pixels
"""
if save_to is not None:
with open(save_to, 'w+') as f:
f.write(output_str)
return output_str
|
from django.conf.urls import patterns, url
from . import views
urlpatterns = patterns(
'',
url('^manifest-revalidation$', views.manifest_revalidation,
name='zadmin.manifest_revalidation'),
)
|
#!/usr/bin/env python
# Copyright (c) 2014 Johns Hopkins University
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# - Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
# - Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the
# distribution.
# - Neither the name of the copyright holders nor the names of
# its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
# THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
# INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
# (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
# STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
# OF THE POSSIBILITY OF SUCH DAMAGE.
import sys
import sqlite3
import random
if __name__ == '__main__':
if len(sys.argv) < 6:
print >> sys.stderr, "Usage: python %s db (cx|sp) src dest failRate"%(sys.argv[0],)
sys.exit(1)
db = sys.argv[1]
setup = sys.argv[2]
src=int(sys.argv[3])
dest=int(sys.argv[4])
fr=float(sys.argv[5])
c = sqlite3.connect(db)
q=''
if setup == 'cx':
q = 'SELECT f FROM CXFS where src=? and dest=? and bw=2'
elif setup=='sp':
q = 'SELECT f FROM sp_thresh_entry where src=? and dest=? and prr=0.99'
elif setup=='spe':
q = 'SELECT f FROM sp_etx_entry where src=? and dest=?'
for (f,) in c.execute(q, (src, dest)).fetchall():
if f == src or f==dest or random.random() > fr:
print "%d r"%(f,)
else:
print "%d q"%(f,)
|
#%% import
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
import numpy as np
import matplotlib.pyplot as plt
import os
#%% prepare chinese character dataset
dataset = keras.preprocessing.image_dataset_from_directory(
"white256", label_mode=None, color_mode='grayscale', image_size=(256, 256), batch_size=32
)
dataset = dataset.map(lambda x: x / 255.0)
#%% discriminator
discriminator = keras.Sequential(
[
keras.Input(shape=(256, 256, 1)),
layers.Conv2D(64, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Conv2D(32, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Conv2D(16, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Conv2D(16, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Flatten(),
layers.Dropout(0.2),
layers.Dense(1, activation="sigmoid"),
],
name="discriminator",
)
discriminator.summary()
#%% generator
latent_dim = 128
generator = keras.Sequential(
[
keras.Input(shape=(latent_dim,)),
layers.Dense(16 * 16 * 128),
layers.Reshape((16, 16, 128)),
layers.Conv2DTranspose(16, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Conv2DTranspose(16, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Conv2DTranspose(32, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Conv2DTranspose(64, kernel_size=4, strides=2, padding="same"),
layers.LeakyReLU(alpha=0.2),
layers.Conv2D(1, kernel_size=5, padding="same", activation="tanh"),
],
name="generator",
)
generator.summary()
#%% model
class GAN(keras.Model):
def __init__(self, discriminator, generator, latent_dim):
super(GAN, self).__init__()
self.discriminator = discriminator
self.generator = generator
self.latent_dim = latent_dim
def compile(self, d_optimizer, g_optimizer, loss_fn):
super(GAN, self).compile()
self.d_optimizer = d_optimizer
self.g_optimizer = g_optimizer
self.loss_fn = loss_fn
self.d_loss_metric = keras.metrics.Mean(name="d_loss")
self.g_loss_metric = keras.metrics.Mean(name="g_loss")
@property
def metrics(self):
return [self.d_loss_metric, self.g_loss_metric]
def train_step(self, real_images):
# Sample random points in the latent space
batch_size = tf.shape(real_images)[0]
random_latent_vectors = tf.random.normal(shape=(batch_size, self.latent_dim))
# Decode them to fake images
generated_images = self.generator(random_latent_vectors)
# Combine them with real images
combined_images = tf.concat([generated_images, real_images], axis=0)
# Assemble labels discriminating real from fake images
labels = tf.concat(
[tf.ones((batch_size, 1)), tf.zeros((batch_size, 1))], axis=0
)
# Add random noise to the labels - important trick!
labels += 0.05 * tf.random.uniform(tf.shape(labels))
# Train the discriminator
with tf.GradientTape() as tape:
predictions = self.discriminator(combined_images)
d_loss = self.loss_fn(labels, predictions)
grads = tape.gradient(d_loss, self.discriminator.trainable_weights)
self.d_optimizer.apply_gradients(
zip(grads, self.discriminator.trainable_weights)
)
# Sample random points in the latent space
random_latent_vectors = tf.random.normal(shape=(batch_size, self.latent_dim))
# Assemble labels that say "all real images"
misleading_labels = tf.zeros((batch_size, 1))
# Train the generator (note that we should *not* update the weights
# of the discriminator)!
with tf.GradientTape() as tape:
predictions = self.discriminator(self.generator(random_latent_vectors))
g_loss = self.loss_fn(misleading_labels, predictions)
grads = tape.gradient(g_loss, self.generator.trainable_weights)
self.g_optimizer.apply_gradients(zip(grads, self.generator.trainable_weights))
# Update metrics
self.d_loss_metric.update_state(d_loss)
self.g_loss_metric.update_state(g_loss)
return {
"d_loss": self.d_loss_metric.result(),
"g_loss": self.g_loss_metric.result(),
}
#%% callback
class GANMonitor(keras.callbacks.Callback):
def __init__(self, num_img=3, latent_dim=128):
self.num_img = num_img
self.latent_dim = latent_dim
def on_epoch_end(self, epoch, logs=None):
random_latent_vectors = tf.random.normal(shape=(self.num_img, self.latent_dim))
generated_images = self.model.generator(random_latent_vectors)
generated_images *= 255
generated_images.numpy()
for i in range(self.num_img):
img = keras.preprocessing.image.array_to_img(generated_images[i])
img.save("6_img_%03d_%d.png" % (epoch, i))
#%% train
epochs = 30
gan = GAN(discriminator=discriminator, generator=generator, latent_dim=latent_dim)
gan.compile(
d_optimizer=keras.optimizers.Adam(learning_rate=0.0002),
g_optimizer=keras.optimizers.Adam(learning_rate=0.0002),
loss_fn=keras.losses.BinaryCrossentropy(),
)
history = gan.fit(
dataset, epochs=epochs, callbacks=[GANMonitor(num_img=10, latent_dim=latent_dim)]
)
#%% plot training metrics
#d_loss
plt.clf()
plt.plot(history.history['d_loss'])
plt.title('Discriminator Loss')
plt.ylabel('Loss')
plt.xlabel('Epoch')
plt.savefig('d_loss.png')
# g_loss
plt.clf()
plt.plot(history.history['g_loss'])
plt.title('Generator Loss')
plt.ylabel('Loss')
plt.xlabel('Epoch')
plt.savefig('g_loss.png') |
#!/usr/bin/env python
# coding: utf-8
# # SMIB system as in Milano's book example 8.1
# In[1]:
import numpy as np
import matplotlib.pyplot as plt
from IPython.core.display import HTML
get_ipython().run_line_magic('config', "InlineBackend.figure_format = 'svg'")
plt.ion()
# In[2]:
get_ipython().run_line_magic('matplotlib', 'widget')
# In[3]:
from pydae import ssa
from smib_milano_ex8p1_4ord import smib_milano_ex8p1_4ord_class
# ### Instantiate system
# In[4]:
smib = smib_milano_ex8p1_4ord_class()
smib.t_end = 15.0
smib.Dt = 0.01
smib.decimation =1
smib.update()
# ### Initialize the system (backward and foreward)
# In[5]:
events=[{'p_t':0.1,'X_line':0.01}]
smib.initialize(events,xy0='xy_0.json')
smib.save_0()
smib.report_x() # obtained dynamic states
smib.report_y() # obtained algebraic states
smib.report_z() # obtained outputs
smib.report_u() # obtained algebraic states (theta is both state and output; f_x is both input and output)
smib.report_params() # considered parameters
# ### Small signal analisys
# In[6]:
ssa.eval_A(smib) # method to linealized the system and to compute matrix A
eig_df=ssa.damp_report(smib) # method to create a pandas.DataFrame after computing eigenvalues for A
eig_df
# In[7]:
ssa.participation(smib).abs().round(2)
# ### Simulation
#
# A time simulation can be performed using the method `simulate`:
# In[8]:
smib.initialize([{'p_t':0.7, 'q_t':0.2}],xy0='xy_0.json')
smib.simulate([{'t_end':1}, # compute initial condition with defined P and Q and run until t=1s
{'t_end':20, 'v_f':2.5}], # compute initial condition with defined P and Q and run until t=1s
'prev');
# In[9]:
# plotting the results with matplolib:
plt.close('all')
fig, axes = plt.subplots(nrows=1,ncols=1, figsize=(6, 3), dpi=100)
axes.plot(smib.T, smib.get_values('p_t') , label=f'$p_t$')
axes.plot(smib.T, smib.get_values('q_t') , label=f'$q_t$')
axes.grid()
axes.set_ylabel('Powers (p.u.)')
axes.set_xlabel('Time (s)')
axes.legend()
fig.tight_layout()
# In[ ]:
# In[10]:
def simulate_fault(system,duration,X_fault=1e-4,N_steps=500):
Dt = smib.struct[0].Dt
Dt_recovery = 10e-6
t_0 = smib.struct[0].t
system.run([{'t_end':t_0+duration,'B_shunt':1/X_fault}])
it = 0.0
for x in np.linspace(0,1.0,N_steps):
#B_shunt = 1/X_fault - x**2/X_fault
B_shunt = 1/X_fault - x/X_fault
B_shunt = 1/X_fault - x**0.5/X_fault
system.run([{'Dt':Dt_recovery/2,'t_end':t_0+duration+it*Dt_recovery,'B_shunt':B_shunt}])
it+=1.0
system.run([{'Dt':Dt_recovery/2,'t_end':t_0+duration+(it+1)*Dt_recovery,'B_shunt':0.0}])
system.run([{'Dt':Dt,'t_end':t_0+duration+Dt,'B_shunt':0.0}])
smib = smib_milano_ex8p1_4ord_class()
smib.initialize([{'p_t':0.8, 'q_t':0.4, 'D':0.0}],1)
smib.run([{'t_end':1}])
simulate_fault(smib,0.05)
smib.run([{'t_end':20}])
smib.post();
# In[11]:
# plotting the results with matplolib:
plt.close('all')
fig, axes = plt.subplots(nrows=3,ncols=1, figsize=(6, 6), dpi=100, sharex=True)
axes[0].plot(smib.T, smib.get_values('v_1') , label=f'$v_1$')
axes[1].plot(smib.T, np.rad2deg(smib.get_values('delta')) , label=f'$\delta$')
axes[2].plot(smib.T, smib.get_values('omega') , label=f'$\omega$')
axes[0].set_ylabel('Powers (p.u.)')
axes[1].set_xlabel('Time (s)')
for ax in axes:
ax.legend()
ax.grid()
fig.tight_layout()
# In[12]:
# plotting the results with matplolib:
plt.close('all')
fig, axes = plt.subplots(nrows=1,ncols=1, figsize=(6, 3), dpi=100)
axes.plot(np.rad2deg(smib.get_values('delta')), smib.get_values('p_m') , label=f'$p_m$')
axes.plot(np.rad2deg(smib.get_values('delta')), smib.get_values('p_t') , label=f'$p_t$')
axes.grid()
axes.set_ylabel('Powers (p.u.)')
axes.set_xlabel('Time (s)')
axes.legend()
fig.tight_layout()
# In[13]:
smib.decimation
# In[14]:
smib.struct[0]['iters'][smib.struct[0]['it']]
# In[139]:
# In[157]:
X_fault = 1e-3
x = np.linspace(0,1.0,200)
B_shunt = 1/X_fault - x**0.5/X_fault
fig, axes = plt.subplots(nrows=1,ncols=1, figsize=(6, 3), dpi=100)
axes.plot(x, B_shunt)
# In[ ]:
# In[74]:
import xml.etree.ElementTree
# In[ ]:
|
from cloudaux.aws.ec2 import describe_images
from cloudaux.aws.ec2 import describe_image_attribute
from cloudaux.decorators import modify_output
from flagpole import FlagRegistry, Flags
registry = FlagRegistry()
FLAGS = Flags('BASE', 'KERNEL', 'RAMDISK', 'LAUNCHPERMISSION', 'PRODUCTCODES')
@registry.register(flag=FLAGS.KERNEL)
def get_kernel(image, **conn):
attribute = describe_image_attribute(
Attribute='kernel', ImageId=image['ImageId'], **conn)
return dict(KernelId=attribute['KernelId'])
@registry.register(flag=FLAGS.RAMDISK)
def get_ramdisk(image, **conn):
attribute = describe_image_attribute(
Attribute='ramdisk', ImageId=image['ImageId'], **conn)
return dict(RamdiskId=attribute['RamdiskId'])
@registry.register(flag=FLAGS.LAUNCHPERMISSION)
def get_launch_permission(image, **conn):
attribute = describe_image_attribute(
Attribute='launchPermission', ImageId=image['ImageId'], **conn)
return dict(LaunchPermissions=attribute['LaunchPermissions'])
@registry.register(flag=FLAGS.PRODUCTCODES)
def get_product_codes(image, **conn):
attribute = describe_image_attribute(
Attribute='productCodes', ImageId=image['ImageId'], **conn)
return dict(ProductCodes=attribute['ProductCodes'])
@registry.register(flag=FLAGS.BASE)
def get_base(image, **conn):
image = describe_images(ImageIds=[image['ImageId']], **conn)
image = image[0]
arn = 'arn:aws:ec2:{region}::image/{imageid}'.format(
region=conn['region'],
imageid=image['ImageId'])
image.update({'Arn': arn, 'Region': conn['region'], '_version': 1})
return image
@modify_output
def get_image(image_id, flags=FLAGS.ALL, **conn):
"""
Orchestrates all the calls required to fully build out an EC2 Image (AMI, AKI, ARI)
{
"Architecture": "x86_64",
"Arn": "arn:aws:ec2:us-east-1::image/ami-11111111",
"BlockDeviceMappings": [],
"CreationDate": "2013-07-11T16:04:06.000Z",
"Description": "...",
"Hypervisor": "xen",
"ImageId": "ami-11111111",
"ImageLocation": "111111111111/...",
"ImageType": "machine",
"KernelId": "aki-88888888",
"LaunchPermissions": [],
"Name": "...",
"OwnerId": "111111111111",
"ProductCodes": [],
"Public": false,
"RamdiskId": {},
"RootDeviceName": "/dev/sda1",
"RootDeviceType": "ebs",
"SriovNetSupport": "simple",
"State": "available",
"Tags": [],
"VirtualizationType": "hvm",
"_version": 1
}
:param image_id: str ami id
:param flags: By default, set to ALL fields
:param conn: dict containing enough information to make a connection to the desired account.
Must at least have 'assume_role' key.
:return: dict containing a fully built out image.
"""
image = dict(ImageId=image_id)
conn['region'] = conn.get('region', 'us-east-1')
return registry.build_out(flags, image, **conn)
|
# see https://github.com/WolfgangFahl/gremlin-python-tutorial/blob/master/test_001.py
from tutorial import remote
# initialize a remote traversal
g = remote.RemoteTraversal().g()
# test the number of vertices
def test_VCount():
vCount=g.V().count().next()
print ("g.V().count=%d" % (vCount))
assert vCount == 6
# test the number of edges
def test_ECount():
eCount=g.E().count().next()
print ("g.E().count=%d" % (eCount))
assert eCount == 6
# call the vertice count test
test_VCount()
# call the edge count test
test_ECount()
|
class NoSuchEventException(Exception):
r""""""
def __init__(self, message=None):
if message is None:
message = "The specified event is not registered."
super(NoSuchEventException, self).__init__(message)
|
# Generates Random char sequence
# The Grabs a random word within a set char length to use as the base
# The char length is based on a difficulty setting
import random
# Shuffles the word in place
def WordScrambler(word):
listWord = list(word)
random.shuffle(listWord)
result = ''.join(listWord)
return result
|
import numpy as np
import torch
import torch.nn as nn
import torch.nn.functional as F
from .util import init, get_clones
from .attention import Encoder
class MLPLayer(nn.Module):
def __init__(self, input_dim, hidden_size, layer_N, use_orthogonal, use_ReLU):
super(MLPLayer, self).__init__()
self._layer_N = layer_N
active_func = [nn.Tanh(), nn.ReLU()][use_ReLU]
init_method = [nn.init.xavier_uniform_, nn.init.orthogonal_][use_orthogonal]
gain = nn.init.calculate_gain(['tanh', 'relu'][use_ReLU])
def init_(m):
return init(m, init_method, lambda x: nn.init.constant_(x, 0), gain=gain)
self.fc1 = nn.Sequential(
init_(nn.Linear(input_dim, hidden_size)), active_func, nn.LayerNorm(hidden_size))
self.fc_h = nn.Sequential(init_(
nn.Linear(hidden_size, hidden_size)), active_func, nn.LayerNorm(hidden_size))
self.fc2 = get_clones(self.fc_h, self._layer_N)
def forward(self, x):
x = self.fc1(x)
for i in range(self._layer_N):
x = self.fc2[i](x)
return x
class CONVLayer(nn.Module):
def __init__(self, input_dim, hidden_size, use_orthogonal, use_ReLU):
super(CONVLayer, self).__init__()
active_func = [nn.Tanh(), nn.ReLU()][use_ReLU]
init_method = [nn.init.xavier_uniform_, nn.init.orthogonal_][use_orthogonal]
gain = nn.init.calculate_gain(['tanh', 'relu'][use_ReLU])
def init_(m):
return init(m, init_method, lambda x: nn.init.constant_(x, 0), gain=gain)
self.conv = nn.Sequential(
init_(nn.Conv1d(in_channels=input_dim, out_channels=hidden_size//4, kernel_size=3, stride=2, padding=0)), active_func, #nn.BatchNorm1d(hidden_size//4),
init_(nn.Conv1d(in_channels=hidden_size//4, out_channels=hidden_size//2, kernel_size=3, stride=1, padding=1)), active_func, #nn.BatchNorm1d(hidden_size//2),
init_(nn.Conv1d(in_channels=hidden_size//2, out_channels=hidden_size, kernel_size=3, stride=1, padding=1)), active_func) #, nn.BatchNorm1d(hidden_size))
def forward(self, x):
x = self.conv(x)
return x
class MLPBase(nn.Module):
def __init__(self, args, obs_shape, cat_self=True, attn_internal=False):
super(MLPBase, self).__init__()
self._use_feature_normalization = args.use_feature_normalization
self._use_feature_popart = args.use_feature_popart
self._use_orthogonal = args.use_orthogonal
self._use_ReLU = args.use_ReLU
self._use_attn = args.use_attn
self._attn_internal = attn_internal
self._use_average_pool = args.use_average_pool
self._use_conv1d = args.use_conv1d
self._stacked_frames = args.stacked_frames
self._layer_N = 0 if args.use_single_network else args.layer_N
self._attn_size = args.attn_size
self.hidden_size = args.hidden_size
assert (self._use_feature_normalization and self._use_feature_popart) == False, (
"--use_feature_normalization and --use_feature_popart can not be set True simultaneously.")
obs_dim = obs_shape[0]
if self._use_feature_popart:
self.feature_norm = PopArt(obs_dim)
if self._use_feature_normalization:
self.feature_norm = nn.LayerNorm(obs_dim)
if self._use_attn and attn_internal:
if self._use_average_pool:
if cat_self:
inputs_dim = self._attn_size + obs_shape[-1][1]
else:
inputs_dim = self._attn_size
else:
split_inputs_dim = 0
split_shape = obs_shape[1:]
for i in range(len(split_shape)):
split_inputs_dim += split_shape[i][0]
inputs_dim = split_inputs_dim * self._attn_size
self.attn = Encoder(args, obs_shape, cat_self)
self.attn_norm = nn.LayerNorm(inputs_dim)
else:
inputs_dim = obs_dim
if self._use_conv1d:
self.conv = CONVLayer(self._stacked_frames, self.hidden_size, self._use_orthogonal, self._use_ReLU)
random_x = torch.FloatTensor(1, self._stacked_frames, inputs_dim//self._stacked_frames)
random_out = self.conv(random_x)
assert len(random_out.shape)==3
inputs_dim = random_out.size(-1) * random_out.size(-2)
self.mlp = MLPLayer(inputs_dim, self.hidden_size,
self._layer_N, self._use_orthogonal, self._use_ReLU)
def forward(self, x):
if self._use_feature_popart or self._use_feature_normalization:
x = self.feature_norm(x)
if self._use_attn and self._attn_internal:
x = self.attn(x, self_idx=-1)
x = self.attn_norm(x)
if self._use_conv1d:
batch_size = x.size(0)
x = x.view(batch_size, self._stacked_frames, -1)
x = self.conv(x)
x = x.view(batch_size, -1)
x = self.mlp(x)
return x |
from markdownTable import markdownTable
import json
with open('idl.json') as f:
idl = json.load(f)
for ins in idl['instructions']:
print('### ' + ins['name'])
print('#### Accounts')
print(markdownTable(ins['accounts']).setParams(row_sep = 'markdown', quote = False).getMarkdown())
if(len(ins['args']) > 0):
print('#### Arguments')
print(markdownTable(ins['args']).setParams(row_sep = 'markdown', quote = False).getMarkdown())
print() |
from django_filters.rest_framework import BaseInFilter, CharFilter, FilterSet
from titles.models import Title
class CharFilterInFilter(BaseInFilter, CharFilter):
pass
class TitleFilter(FilterSet):
category = CharFilterInFilter(
field_name='category__slug',
lookup_expr='in'
)
genre = CharFilterInFilter(
field_name='genre__slug',
lookup_expr='in'
)
name = CharFilter(
field_name='name',
lookup_expr='contains'
)
class Meta:
model = Title
fields = ('category', 'genre', 'name', 'year')
|
import xml.etree.ElementTree
import os
files = os.listdir('feature_points')
categories = {}
types = {}
cn = 0
t = 0
m = []
classes = {}
cl = 0
y = []
indices = {}
ind = 0
for f in files:
name = f
if name[0] not in classes:
classes[name[0]] = cl
cl = cl + 1
y.append(classes[name[0]])
root = xml.etree.ElementTree.parse('feature_points/' + name).getroot()
attributes = [x.attrib for x in root.iter('FeaturePoint')]
l = []
for a in attributes:
if a['category'] + a['type'] not in indices:
indices[a['category'] + a['type']] = ind
ind = ind + 1
if a['category'] not in categories:
categories[a['category']] = cn
cn = cn + 1
if a['type'] not in types:
types[a['type']] = t
t = t + 1
matrix = []
for f in files:
name = f
root = xml.etree.ElementTree.parse('feature_points/' + name).getroot()
attributes = [x.attrib for x in root.iter('FeaturePoint')]
l = 100 * [0]
for a in attributes:
j = indices[a['category'] + a['type']]
l[4 * j + 0] = a['x']
l[4 * j + 1] = a['y']
l[4 * j + 2] = categories[a['category']]
l[4 * j + 2] = types[a['type']]
matrix.append(l)
with open('data.txt', 'w') as f:
for i in range(len(matrix)):
f.write(' '.join([str(x) for x in matrix[i]]) + ' ' + str(y[i]) + '\n')
|
#!/usr/bin/python3.5
# -*- coding utf-8
|
import json
import os
from django.core.management.base import BaseCommand
from home.models import ReplicaSet, DownloadLocation
from wcd_pth_migration.utils import generate_spectrals_for_dir
class Command(BaseCommand):
help = 'Clears the database of what torrents, trans torrents, also removes all torrents from transmission'
def handle(self, *args, **options):
checked = []
try:
with open('checked.json', 'r') as f:
checked = json.loads(f.read())
except IOError:
pass
for dl in DownloadLocation.objects.filter(zone=ReplicaSet.ZONE_WHAT):
for torrent in os.listdir(dl.path):
if torrent in checked:
print 'Already checked', torrent, 'skipping...'
continue
torrent_path = os.path.join(dl.path, torrent)
print 'Generating spectrals for', torrent_path
if not generate_spectrals_for_dir(torrent_path):
print 'There are no FLACs, moving on...'
else:
raw_input('Please check the spectrals...')
checked.append(torrent)
with open('checked.json', 'w') as f:
f.write(json.dumps(checked))
|
# -*- coding: utf-8 -*-
from unittest import TestCase
from ..number_token import (
gen_float_token_with_digit,
gen_int_token_with_digit,
sub_token_with_value_sequentially,
NumberToken,
)
class NumberTokenTestCase(TestCase):
def run_test_denormalizable(self, test_cases, normalizer):
for test_case in test_cases:
with self.subTest(test_case=test_case):
self.assertEqual(
test_case[1],
normalizer.normalize(test_case[0]),
)
self.assertEqual(
test_case[0],
normalizer.denormalize(
sentence=test_case[1][0],
meta=test_case[1][1],
),
)
def run_test_not_denormalizable(self, test_cases, normalizer):
for test_case in test_cases:
with self.subTest(test_case=test_case):
self.assertEqual(
test_case[1],
normalizer.normalize(test_case[0]),
)
self.assertEqual(
test_case[1][0],
normalizer.denormalize(
sentence=test_case[1][0],
meta=test_case[1][1],
),
)
def test_gen_float_token_with_digit(self):
self.assertEqual(
["_1float1_", "_1float5_", "_3float4_", "_4float2_"],
gen_float_token_with_digit(
["2.0", "0.00003", "300.1113", "5000.05"]),
)
def test_gen_int_token_with_digit(self):
self.assertEqual(
["_1int_", "_2int_", "_3int_", "_7int_"],
gen_int_token_with_digit(["1", "20", "300", "5000.05"]),
)
def test_sub_token_with_value_sequentially(self):
test_cases = [
(
{
"sentence": "A@A@@A@@@AA",
"token": "A",
"value_list": ["1", "2", "3", "4", "5"],
},
"1@2@@3@@@45",
),
(
{
"sentence": "來亂的",
"token": "bla",
"value_list": [],
},
"來亂的",
),
]
for test_case in test_cases:
with self.subTest(test_case=test_case):
self.assertEqual(
test_case[1],
sub_token_with_value_sequentially(**test_case[0]),
)
def test_unhandle_case(self):
with self.assertRaises(KeyError):
NumberToken(token="_ohoh_")
def test_pure_int(self):
int_text_normalizer = NumberToken(token="_int_")
test_cases = [
("123", ("_int_", {"_int_": ["123"]})),
("23.35", ("_int_._int_", {"_int_": ["23", "35"]})),
("23 0000", ("_int_ _int_", {"_int_": ["23", "0000"]})),
("OHOH 23", ("OHOH _int_", {"_int_": ["23"]})),
("122223333 OHOH", ("_int_ OHOH", {"_int_": ["122223333"]})),
("１００", ("_int_", {"_int_": ["１００"]})),
("3４0分", ("_int_分", {"_int_": ["3４0"]})),
("薄餡大大１個打10個", ("薄餡大大_int_個打_int_個", {"_int_": ["１", "10"]})),
("0８00-２２-44-６６",
("_int_-_int_-_int_-_int_", {"_int_": ["0８00", "２２", "44", "６６"]})),
("來亂的", ("來亂的", {"_int_": []})),
]
self.run_test_denormalizable(
normalizer=int_text_normalizer,
test_cases=test_cases,
)
def test_pure_int_not_denormalizable(self):
int_text_normalizer_not_denormalizable = NumberToken(
token="_int_",
denormalizable=False,
)
test_cases = [
("123", ("_int_", None)),
("23.35", ("_int_._int_", None)),
("23 0000", ("_int_ _int_", None)),
("OHOH 23", ("OHOH _int_", None)),
("122223333 OHOH", ("_int_ OHOH", None)),
("１００", ("_int_", None)),
("3４0分", ("_int_分", None)),
("薄餡大大１個打10個", ("薄餡大大_int_個打_int_個", None)),
("0８00-２２-44-６６", ("_int_-_int_-_int_-_int_", None)),
("來亂的", ("來亂的", None)),
]
self.run_test_not_denormalizable(
normalizer=int_text_normalizer_not_denormalizable,
test_cases=test_cases,
)
def test_pure_float(self):
float_text_normalizer = NumberToken(token="_float_")
test_cases = [
("49.3", ("_float_", {"_float_": ["49.3"]})),
("12.33 456.0", ("_float_ _float_", {"_float_": ["12.33", "456.0"]})),
("123", ("123", {"_float_": []})),
("94.87分", ("_float_分", {"_float_": ["94.87"]})),
("薄餡大大1.5個打10.7個",
("薄餡大大_float_個打_float_個", {"_float_": ["1.5", "10.7"]})),
("123.456.789", ("123.456.789", {"_float_": []})),
("1０0.0００", ("_float_", {"_float_": ["1０0.0００"]})),
("９4.87分", ("_float_分", {"_float_": ["９4.87"]})),
("薄餡大大1.5個打１０.７個",
("薄餡大大_float_個打_float_個", {"_float_": ["1.5", "１０.７"]})),
("１２３.４５６.７８９", ("１２３.４５６.７８９", {"_float_": []})),
("來亂的", ("來亂的", {"_float_": []})),
]
self.run_test_denormalizable(
normalizer=float_text_normalizer,
test_cases=test_cases,
)
def test_pure_float_not_denormalizable(self):
float_text_normalizer = NumberToken(
token="_float_",
denormalizable=False,
)
test_cases = [
("49.3", ("_float_", None)),
("12.33 456.0", ("_float_ _float_", None)),
("123", ("123", None)),
("94.87分", ("_float_分", None)),
("薄餡大大1.5個打10.7個", ("薄餡大大_float_個打_float_個", None)),
("123.456.789", ("123.456.789", None)),
("1０0.0００", ("_float_", None)),
("９4.87分", ("_float_分", None)),
("薄餡大大1.5個打１０.７個", ("薄餡大大_float_個打_float_個", None)),
("１２３.４５６.７８９", ("１２３.４５６.７８９", None)),
("來亂的", ("來亂的", None)),
]
self.run_test_not_denormalizable(
normalizer=float_text_normalizer,
test_cases=test_cases,
)
def test_int_with_digit(self):
intd_text_normalizer = NumberToken(token="_{}int_")
test_cases = [
("123", ("_3int_", {"_3int_": ["123"]})),
("098765431389", ("_12int_", {"_12int_": ["098765431389"]})),
("1 4567890103",
("_1int_ _10int_", {"_1int_": ["1"], "_10int_": ["4567890103"]})),
("_12float733_", ("_12float733_", {})),
("ohoh 000 _33float0_ 1",
("ohoh _3int_ _33float0_ _1int_", {"_3int_": ["000"], "_1int_": ["1"]})),
("123 345 678 901",
("_3int_ _3int_ _3int_ _3int_", {"_3int_": ["123", "345", "678", "901"]})),
("１００", ("_3int_", {"_3int_": ["１００"]})),
("3４0分", ("_3int_分", {"_3int_": ["3４0"]})),
("薄餡大大１個打10個", ("薄餡大大_1int_個打_2int_個", {"_1int_": ["１"], "_2int_": ["10"]})),
("0８00-２２-44-６６",
("_4int_-_2int_-_2int_-_2int_",
{"_4int_": ["0８00"], "_2int_": ["２２", "44", "６６"]})),
("來亂的", ("來亂的", {})),
]
self.run_test_denormalizable(
test_cases=test_cases,
normalizer=intd_text_normalizer,
)
def test_int_with_digit_not_denormalizable(self):
intd_text_normalizer = NumberToken(
token="_{}int_",
denormalizable=False,
)
test_cases = [
("123", ("_3int_", None)),
("098765431389", ("_12int_", None)),
("1 4567890103", ("_1int_ _10int_", None)),
("_12float733_", ("_12float733_", None)),
("ohoh 000 _33float0_ 1", ("ohoh _3int_ _33float0_ _1int_", None)),
("１００", ("_3int_", None)),
("3４0分", ("_3int_分", None)),
("薄餡大大１個打10個", ("薄餡大大_1int_個打_2int_個", None)),
("0８00-２２-44-６６", ("_4int_-_2int_-_2int_-_2int_", None)),
("來亂的", ("來亂的", None)),
]
self.run_test_not_denormalizable(
test_cases=test_cases,
normalizer=intd_text_normalizer,
)
def test_float_with_digit(self):
floatd_text_normalizer = NumberToken(
token="_{}float{}_",
)
test_cases = [
("123.33", ("_3float2_", {"_3float2_": ["123.33"]})),
("123", ("123", {})),
("1234567890.123456789011",
("_10float12_", {"_10float12_": ["1234567890.123456789011"]})),
("1.3 224.00", ("_1float1_ _3float2_",
{"_1float1_": ["1.3"], "_3float2_": ["224.00"]})),
("12.3 34.5 67.8 90.1",
("_2float1_ _2float1_ _2float1_ _2float1_",
{"_2float1_": ["12.3", "34.5", "67.8", "90.1"]})),
("_3int_", ("_3int_", {})),
("94.87分", ("_2float2_分", {"_2float2_": ["94.87"]})),
("薄餡大大1.5個打10.7個",
("薄餡大大_1float1_個打_2float1_個",
{"_1float1_": ["1.5"], "_2float1_": ["10.7"]})),
("123.456.789", ("123.456.789", {})),
("1０0.0００", ("_3float3_", {"_3float3_": ["1０0.0００"]})),
("９4.87分", ("_2float2_分", {"_2float2_": ["９4.87"]})),
("薄餡大大1.5個打１０.７個",
("薄餡大大_1float1_個打_2float1_個",
{"_1float1_": ["1.5"], "_2float1_": ["１０.７"]})),
("１２３.４５６.７８９", ("１２３.４５６.７８９", {})),
("來亂的", ("來亂的", {})),
]
self.run_test_denormalizable(
test_cases=test_cases,
normalizer=floatd_text_normalizer,
)
def test_float_with_digit_not_denrmalizable(self):
floatd_text_normalizer = NumberToken(
token="_{}float{}_",
denormalizable=False,
)
test_cases = [
("123.33", ("_3float2_", None)),
("123", ("123", None)),
("1234567890.123456789011", ("_10float12_", None)),
("1.3 224.00", ("_1float1_ _3float2_", None)),
("_3int_", ("_3int_", None)),
("94.87分", ("_2float2_分", None)),
("薄餡大大1.5個打10.7個", ("薄餡大大_1float1_個打_2float1_個", None)),
("123.456.789", ("123.456.789", None)),
("1０0.0００", ("_3float3_", None)),
("９4.87分", ("_2float2_分", None)),
("薄餡大大1.5個打１０.７個", ("薄餡大大_1float1_個打_2float1_個", None)),
("１２３.４５６.７８９", ("１２３.４５６.７８９", None)),
("來亂的", ("來亂的", None)),
]
self.run_test_not_denormalizable(
test_cases=test_cases,
normalizer=floatd_text_normalizer,
)
def test_int_text_normalizer_with_space(self):
int_text_normalizer_with_space = NumberToken(token=" _int_ ")
test_cases = [
("12345678900", (" _int_ ", {" _int_ ": ["12345678900"]})),
("340分", (" _int_ 分", {" _int_ ": ["340"]})),
("薄餡大大1個打10個", ("薄餡大大 _int_ 個打 _int_ 個", {" _int_ ": ["1", "10"]})),
("0800-22-44-66", (" _int_ - _int_ - _int_ - _int_ ",
{" _int_ ": ["0800", "22", "44", "66"]})),
("１００", (" _int_ ", {" _int_ ": ["１００"]})),
("3４0分", (" _int_ 分", {" _int_ ": ["3４0"]})),
("薄餡大大１個打10個", ("薄餡大大 _int_ 個打 _int_ 個", {" _int_ ": ["１", "10"]})),
("0８00-２２-44-６６", (" _int_ - _int_ - _int_ - _int_ ",
{" _int_ ": ["0８00", "２２", "44", "６６"]})),
("家豪大大亂入", ("家豪大大亂入", {" _int_ ": []})),
]
self.run_test_denormalizable(
test_cases=test_cases,
normalizer=int_text_normalizer_with_space,
)
with self.assertRaises(ValueError):
int_text_normalizer_with_space.denormalize(
sentence=" _int_ 和 _int_ 這兩個日期都沒有雞排",
meta={" _int_ ": ["12"]},
)
def test_float_text_normalizer_with_space(self):
float_text_normalizer_with_space = NumberToken(token=" _float_ ")
test_cases = [
("100.000", (" _float_ ", {" _float_ ": ["100.000"]})),
("94.87分", (" _float_ 分", {" _float_ ": ["94.87"]})),
("薄餡大大1.5個打10.7個", ("薄餡大大 _float_ 個打 _float_ 個", {" _float_ ": ["1.5", "10.7"]})),
("123.456.789", ("123.456.789", {" _float_ ": []})),
("1０0.0００", (" _float_ ", {" _float_ ": ["1０0.0００"]})),
("９4.87分", (" _float_ 分", {" _float_ ": ["９4.87"]})),
("薄餡大大1.5個打１０.７個", ("薄餡大大 _float_ 個打 _float_ 個", {" _float_ ": ["1.5", "１０.７"]})),
("１２３.４５６.７８９", ("１２３.４５６.７８９", {" _float_ ": []})),
("家豪大大亂入", ("家豪大大亂入", {" _float_ ": []})),
]
self.run_test_denormalizable(
test_cases=test_cases,
normalizer=float_text_normalizer_with_space,
)
def test_int_with_digit_n_space(self):
intd_text_normalizer_with_space = NumberToken(token=" _{}int_ ")
test_cases = [
("123", (" _3int_ ", {" _3int_ ": ["123"]})),
("098765431389", (" _12int_ ", {" _12int_ ": ["098765431389"]})),
("1 4567890103",
(" _1int_ _10int_ ",
{" _1int_ ": ["1"], " _10int_ ": ["4567890103"]})),
("_12float733_", ("_12float733_", {})),
("ohoh 000 _33float0_ 1",
("ohoh _3int_ _33float0_ _1int_ ",
{" _3int_ ": ["000"], " _1int_ ": ["1"]})),
("123 345 678 901",
(" _3int_ _3int_ _3int_ _3int_ ",
{" _3int_ ": ["123", "345", "678", "901"]})),
("１００", (" _3int_ ", {" _3int_ ": ["１００"]})),
("3４0分", (" _3int_ 分", {" _3int_ ": ["3４0"]})),
("薄餡大大１個打10個",
("薄餡大大 _1int_ 個打 _2int_ 個",
{" _1int_ ": ["１"], " _2int_ ": ["10"]})),
("0８00-２２-44-６６",
(" _4int_ - _2int_ - _2int_ - _2int_ ",
{" _4int_ ": ["0８00"], " _2int_ ": ["２２", "44", "６６"]})),
("來亂的", ("來亂的", {})),
]
self.run_test_denormalizable(
test_cases=test_cases,
normalizer=intd_text_normalizer_with_space,
)
def test_float_with_digit_n_space(self):
floatd_text_normalizer_with_space = NumberToken(
token=" _{}float{}_ ",
)
test_cases = [
("123.33", (" _3float2_ ", {" _3float2_ ": ["123.33"]})),
("123", ("123", {})),
("1234567890.123456789011",
(" _10float12_ ", {" _10float12_ ": ["1234567890.123456789011"]})),
("1.3 224.00", (" _1float1_ _3float2_ ",
{" _1float1_ ": ["1.3"], " _3float2_ ": ["224.00"]})),
("12.3 34.5 67.8 90.1",
(" _2float1_ _2float1_ _2float1_ _2float1_ ",
{" _2float1_ ": ["12.3", "34.5", "67.8", "90.1"]})),
("_3int_", ("_3int_", {})),
("94.87分", (" _2float2_ 分", {" _2float2_ ": ["94.87"]})),
("薄餡大大1.5個打10.7個",
("薄餡大大 _1float1_ 個打 _2float1_ 個",
{" _1float1_ ": ["1.5"], " _2float1_ ": ["10.7"]})),
("123.456.789", ("123.456.789", {})),
("1０0.0００", (" _3float3_ ", {" _3float3_ ": ["1０0.0００"]})),
("９4.87分", (" _2float2_ 分", {" _2float2_ ": ["９4.87"]})),
("薄餡大大1.5個打１０.７個",
("薄餡大大 _1float1_ 個打 _2float1_ 個",
{" _1float1_ ": ["1.5"], " _2float1_ ": ["１０.７"]})),
("１２３.４５６.７８９", ("１２３.４５６.７８９", {})),
("來亂的", ("來亂的", {})),
]
self.run_test_denormalizable(
test_cases=test_cases,
normalizer=floatd_text_normalizer_with_space,
)
|
from radixlib.api_types.identifiers import AccountIdentifier
from radixlib.api_types.token_amount import TokenAmount
from radixlib.serializable import Serializable
from typing import Optional, Dict, Any
import radixlib as radix
import json
class CreateTokenDefinition(Serializable):
""" Defines a CreateTokenDefinition action """
def __init__(
self,
name: str,
symbol: str,
description: str,
icon_url: str,
url: str,
granularity: int,
token_rri: str,
is_supply_mutable: bool,
owner: Optional[str] = None,
token_supply: Optional[int] = None,
to_account: Optional[str] = None,
) -> None:
""" Instantiates a new CreateTokenDefinition action used for the creation of new tokens.
Args:
owner (str, optional): An account identifier of the account which will be the owner of
the token.
name (str): The name of the token we're creating
symbol (str): The symbol which is a 3 to 8 letters symbol for tokens.
description (str): The description of the token.
icon_url (str): A string of the URL to the token's image.
url (str): A string of the URL to the token itself (could be a website with more info
on the token, or other related info)
granularity (str): A string of the token granularity.
token_rri (str): The Radix Resource Identifier that the token will be created under.
Needs to be derived from the public key of the creator of the token and the HRP of
the specific network.
is_supply_mutable (bool): A boolean which defines whether the supply of the token is
mutable or not. If true, the token can be minted and burned by the owner of the
token. If false the token will have a fixed supply. If this argument is false,
(fixed supply) then the token_supply and to_account arguments need to be specified.
token_supply (int, optional): An optional argument which defaults to None. If the
is_supply_mutable is false, then this argument needs to be supplied.
to_account (str, optional): An optional argument which defaults to None, and defines the
account to send the fixed supply tokens to.
Raises:
ValueError: A value error is raised in the following two cases::
#. When the token supply or the to account are supplied when is_supply_mutable is
True
#. When the token supply or the to_account are not supplied when the
is_supply_mutable is False
#. When the symbol given is not all lower case.
#. When the symbol's length is not between 3 and 8.
#. When the protocol being used for the URLs is not specified
"""
# Checking for incorrect usage of the to_account and token_supply arguments
if is_supply_mutable and (token_supply is not None or to_account is not None or owner is None):
raise ValueError(
"You've specified that the token should be mutable and supplied a value to the "
"'token_supply' or the 'to_account' arguments which is an invalid operation. When "
"creating a mutable token (i.e. is_supply_mutable = True) do not supply anything to "
"the 'token_supply' and 'to_account' arguments"
)
elif not is_supply_mutable and (token_supply is None or to_account is None or owner is not None):
raise ValueError(
"You must specify 'token_supply' and the 'to_account' arguments when creating a "
"fixed supply token and remove the specification for the token owner."
)
# Checking if the provided symbol for the token is valid
if not symbol.islower():
raise ValueError("Token symbols must be all lower case letters.")
if not (2 <= len(symbol) <= 8):
raise ValueError(f"Token symbols must be 2 to 8 characters long.")
# Check that the URLs contain the protocol used.
for url_item in [url, icon_url]:
if url_item and "://" not in url_item:
raise ValueError("When a URL is specified you need to provide the protocol being used.")
self.owner: Optional[AccountIdentifier] = AccountIdentifier(owner) if owner is not None else None
self.name: str = name
self.symbol: str = symbol
self.description: str = description
self.icon_url: str = icon_url
self.url: str = url
self.granularity: int = granularity
self.token_rri: str = token_rri
self.is_supply_mutable: bool = is_supply_mutable
self.token_supply: int = token_supply if token_supply is not None else 0
self.to_account: Optional[AccountIdentifier] = AccountIdentifier(to_account) if to_account is not None else None
def to_dict(self) -> Dict[str, Any]:
"""" Converts the object to a dictionary """
return radix.utils.remove_none_values_recursively(
radix.utils.convert_to_dict_recursively({ # type: ignore
"type": "CreateTokenDefinition",
"to_account": self.to_account,
"token_supply": TokenAmount(
rri = self.token_rri,
amount = self.token_supply
),
"token_properties": {
"name": self.name,
"description": self.description,
"icon_url": self.icon_url,
"url": self.url,
"symbol": self.symbol,
"is_supply_mutable": self.is_supply_mutable,
"granularity": str(int(self.granularity)),
"owner": self.owner
}
})
)
def to_json_string(self) -> str:
""" Converts the object to a JSON string """
return json.dumps(self.to_dict())
@classmethod
def from_dict(
cls,
dictionary: Dict[Any, Any]
) -> 'CreateTokenDefinition':
""" Loads a CreateTokenDefinition from a Gateway API response dictionary
Args:
dictionary (dict): The dictionary to load the object from
Returns:
CreateTokenDefinition: A new CreateTokenDefinition initalized from the dictionary
Raises:
TypeError: Raised when the type of the action in the dictionary does not match
the action name of the class
"""
if dictionary.get('type') != "CreateTokenDefinition":
raise TypeError(f"Expected a dictionary with a type of CreateTokenDefinition but got: {dictionary.get('type')}")
return cls(
owner = None if dictionary['token_properties'].get('owner') is None else dictionary['token_properties']['owner']['address'],
name = dictionary['token_properties']['name'],
symbol = dictionary['token_properties']['symbol'],
description = dictionary['token_properties']['description'],
icon_url = dictionary['token_properties']['icon_url'],
url = dictionary['token_properties']['url'],
granularity = int(dictionary['token_properties']['granularity']),
token_rri = dictionary['token_supply']['token_identifier']['rri'],
is_supply_mutable = dictionary['token_properties']['is_supply_mutable'],
token_supply = None if dictionary['token_properties']['is_supply_mutable'] else int(dictionary['token_supply']['value']),
to_account = None if dictionary.get('to_account') is None else dictionary['to_account']['address']
)
@classmethod
def from_json_string(
cls,
json_string: str
) -> 'CreateTokenDefinition':
""" Loads a CreateTokenDefinition from a Gateway API response JSON string. """
return cls.from_dict(json.loads(json_string)) |
# -*- coding: utf-8 -*-
# Form implementation generated from reading ui file 'mainWin.ui'
#
# Created by: PyQt5 UI code generator 5.11.3
#
# WARNING! All changes made in this file will be lost!
from PyQt5 import QtCore, QtGui, QtWidgets
class Ui_MainWin(object):
def setupUi(self, MainWin):
MainWin.setObjectName("MainWin")
MainWin.resize(896, 694)
self.verticalLayout = QtWidgets.QVBoxLayout(MainWin)
self.verticalLayout.setObjectName("verticalLayout")
self.groupBox = QtWidgets.QGroupBox(MainWin)
self.groupBox.setObjectName("groupBox")
self.horizontalLayout_4 = QtWidgets.QHBoxLayout(self.groupBox)
self.horizontalLayout_4.setObjectName("horizontalLayout_4")
self.gbxOpType = QtWidgets.QGroupBox(self.groupBox)
self.gbxOpType.setObjectName("gbxOpType")
self.horizontalLayout = QtWidgets.QHBoxLayout(self.gbxOpType)
self.horizontalLayout.setObjectName("horizontalLayout")
self.rabAdd = QtWidgets.QRadioButton(self.gbxOpType)
self.rabAdd.setObjectName("rabAdd")
self.horizontalLayout.addWidget(self.rabAdd)
self.rabSub = QtWidgets.QRadioButton(self.gbxOpType)
self.rabSub.setObjectName("rabSub")
self.horizontalLayout.addWidget(self.rabSub)
self.rabMult = QtWidgets.QRadioButton(self.gbxOpType)
self.rabMult.setObjectName("rabMult")
self.horizontalLayout.addWidget(self.rabMult)
self.rabDiv = QtWidgets.QRadioButton(self.gbxOpType)
self.rabDiv.setObjectName("rabDiv")
self.horizontalLayout.addWidget(self.rabDiv)
self.horizontalLayout_4.addWidget(self.gbxOpType)
self.gbxOpStep = QtWidgets.QGroupBox(self.groupBox)
self.gbxOpStep.setObjectName("gbxOpStep")
self.horizontalLayout_2 = QtWidgets.QHBoxLayout(self.gbxOpStep)
self.horizontalLayout_2.setObjectName("horizontalLayout_2")
self.rabOneStep = QtWidgets.QRadioButton(self.gbxOpStep)
self.rabOneStep.setObjectName("rabOneStep")
self.horizontalLayout_2.addWidget(self.rabOneStep)
self.rabTwoStep = QtWidgets.QRadioButton(self.gbxOpStep)
self.rabTwoStep.setObjectName("rabTwoStep")
self.horizontalLayout_2.addWidget(self.rabTwoStep)
self.ranTreeStep = QtWidgets.QRadioButton(self.gbxOpStep)
self.ranTreeStep.setObjectName("ranTreeStep")
self.horizontalLayout_2.addWidget(self.ranTreeStep)
self.horizontalLayout_4.addWidget(self.gbxOpStep)
self.gbxSubjectType = QtWidgets.QGroupBox(self.groupBox)
self.gbxSubjectType.setObjectName("gbxSubjectType")
self.horizontalLayout_3 = QtWidgets.QHBoxLayout(self.gbxSubjectType)
self.horizontalLayout_3.setObjectName("horizontalLayout_3")
self.rabResult = QtWidgets.QRadioButton(self.gbxSubjectType)
self.rabResult.setObjectName("rabResult")
self.horizontalLayout_3.addWidget(self.rabResult)
self.rabItem = QtWidgets.QRadioButton(self.gbxSubjectType)
self.rabItem.setObjectName("rabItem")
self.horizontalLayout_3.addWidget(self.rabItem)
self.horizontalLayout_4.addWidget(self.gbxSubjectType)
self.verticalLayout.addWidget(self.groupBox)
self.groupBox_5 = QtWidgets.QGroupBox(MainWin)
self.groupBox_5.setObjectName("groupBox_5")
self.horizontalLayout_6 = QtWidgets.QHBoxLayout(self.groupBox_5)
self.horizontalLayout_6.setObjectName("horizontalLayout_6")
self.groupBox_6 = QtWidgets.QGroupBox(self.groupBox_5)
self.groupBox_6.setObjectName("groupBox_6")
self.horizontalLayout_5 = QtWidgets.QHBoxLayout(self.groupBox_6)
self.horizontalLayout_5.setObjectName("horizontalLayout_5")
self.btnOpResSet = QtWidgets.QPushButton(self.groupBox_6)
self.btnOpResSet.setMinimumSize(QtCore.QSize(0, 30))
self.btnOpResSet.setObjectName("btnOpResSet")
self.horizontalLayout_5.addWidget(self.btnOpResSet)
self.btnOperatorSet = QtWidgets.QPushButton(self.groupBox_6)
self.btnOperatorSet.setMinimumSize(QtCore.QSize(0, 30))
self.btnOperatorSet.setObjectName("btnOperatorSet")
self.horizontalLayout_5.addWidget(self.btnOperatorSet)
self.horizontalLayout_6.addWidget(self.groupBox_6)
self.ckbBracket = QtWidgets.QCheckBox(self.groupBox_5)
self.ckbBracket.setObjectName("ckbBracket")
self.horizontalLayout_6.addWidget(self.ckbBracket)
self.verticalLayout.addWidget(self.groupBox_5)
self.horizontalLayout_11 = QtWidgets.QHBoxLayout()
self.horizontalLayout_11.setObjectName("horizontalLayout_11")
self.gbxAddSet = QtWidgets.QGroupBox(MainWin)
self.gbxAddSet.setObjectName("gbxAddSet")
self.horizontalLayout_7 = QtWidgets.QHBoxLayout(self.gbxAddSet)
self.horizontalLayout_7.setObjectName("horizontalLayout_7")
self.rabRandCarry = QtWidgets.QRadioButton(self.gbxAddSet)
self.rabRandCarry.setObjectName("rabRandCarry")
self.horizontalLayout_7.addWidget(self.rabRandCarry)
self.rabAddCarry = QtWidgets.QRadioButton(self.gbxAddSet)
self.rabAddCarry.setObjectName("rabAddCarry")
self.horizontalLayout_7.addWidget(self.rabAddCarry)
self.rabNoCarry = QtWidgets.QRadioButton(self.gbxAddSet)
self.rabNoCarry.setObjectName("rabNoCarry")
self.horizontalLayout_7.addWidget(self.rabNoCarry)
self.horizontalLayout_11.addWidget(self.gbxAddSet)
self.gbxSubSet = QtWidgets.QGroupBox(MainWin)
self.gbxSubSet.setObjectName("gbxSubSet")
self.horizontalLayout_8 = QtWidgets.QHBoxLayout(self.gbxSubSet)
self.horizontalLayout_8.setObjectName("horizontalLayout_8")
self.rabRandAbdicate = QtWidgets.QRadioButton(self.gbxSubSet)
self.rabRandAbdicate.setObjectName("rabRandAbdicate")
self.horizontalLayout_8.addWidget(self.rabRandAbdicate)
self.rabSubAbdicate = QtWidgets.QRadioButton(self.gbxSubSet)
self.rabSubAbdicate.setObjectName("rabSubAbdicate")
self.horizontalLayout_8.addWidget(self.rabSubAbdicate)
self.rabNoAbdicate = QtWidgets.QRadioButton(self.gbxSubSet)
self.rabNoAbdicate.setObjectName("rabNoAbdicate")
self.horizontalLayout_8.addWidget(self.rabNoAbdicate)
self.horizontalLayout_11.addWidget(self.gbxSubSet)
self.verticalLayout.addLayout(self.horizontalLayout_11)
self.groupBox_9 = QtWidgets.QGroupBox(MainWin)
self.groupBox_9.setObjectName("groupBox_9")
self.horizontalLayout_9 = QtWidgets.QHBoxLayout(self.groupBox_9)
self.horizontalLayout_9.setObjectName("horizontalLayout_9")
self.label = QtWidgets.QLabel(self.groupBox_9)
self.label.setMaximumSize(QtCore.QSize(80, 16777215))
self.label.setObjectName("label")
self.horizontalLayout_9.addWidget(self.label)
self.spbSubjectCount = QtWidgets.QSpinBox(self.groupBox_9)
self.spbSubjectCount.setMinimumSize(QtCore.QSize(0, 22))
self.spbSubjectCount.setMaximumSize(QtCore.QSize(100, 16777215))
self.spbSubjectCount.setMinimum(1)
self.spbSubjectCount.setMaximum(999)
self.spbSubjectCount.setObjectName("spbSubjectCount")
self.horizontalLayout_9.addWidget(self.spbSubjectCount)
self.btnAddSubject = QtWidgets.QPushButton(self.groupBox_9)
self.btnAddSubject.setMinimumSize(QtCore.QSize(0, 30))
self.btnAddSubject.setObjectName("btnAddSubject")
self.horizontalLayout_9.addWidget(self.btnAddSubject)
self.btnClearSubject = QtWidgets.QPushButton(self.groupBox_9)
self.btnClearSubject.setMinimumSize(QtCore.QSize(0, 30))
self.btnClearSubject.setObjectName("btnClearSubject")
self.horizontalLayout_9.addWidget(self.btnClearSubject)
self.verticalLayout.addWidget(self.groupBox_9)
self.groupBox_10 = QtWidgets.QGroupBox(MainWin)
self.groupBox_10.setMaximumSize(QtCore.QSize(16777215, 200))
self.groupBox_10.setObjectName("groupBox_10")
self.horizontalLayout_10 = QtWidgets.QHBoxLayout(self.groupBox_10)
self.horizontalLayout_10.setObjectName("horizontalLayout_10")
self.txbContent = QtWidgets.QTextBrowser(self.groupBox_10)
self.txbContent.setObjectName("txbContent")
self.horizontalLayout_10.addWidget(self.txbContent)
self.verticalLayout.addWidget(self.groupBox_10)
self.groupBox_11 = QtWidgets.QGroupBox(MainWin)
self.groupBox_11.setObjectName("groupBox_11")
self.gridLayout = QtWidgets.QGridLayout(self.groupBox_11)
self.gridLayout.setObjectName("gridLayout")
self.lneSubTitle = QtWidgets.QLineEdit(self.groupBox_11)
self.lneSubTitle.setMinimumSize(QtCore.QSize(0, 22))
self.lneSubTitle.setObjectName("lneSubTitle")
self.gridLayout.addWidget(self.lneSubTitle, 1, 5, 1, 3)
self.spbColCount = QtWidgets.QSpinBox(self.groupBox_11)
self.spbColCount.setMinimumSize(QtCore.QSize(0, 22))
self.spbColCount.setMinimum(1)
self.spbColCount.setMaximum(5)
self.spbColCount.setObjectName("spbColCount")
self.gridLayout.addWidget(self.spbColCount, 0, 4, 1, 1)
self.btnBrowse = QtWidgets.QPushButton(self.groupBox_11)
self.btnBrowse.setObjectName("btnBrowse")
self.gridLayout.addWidget(self.btnBrowse, 0, 7, 1, 1)
self.spbTotal = QtWidgets.QSpinBox(self.groupBox_11)
self.spbTotal.setMinimumSize(QtCore.QSize(60, 22))
self.spbTotal.setObjectName("spbTotal")
self.gridLayout.addWidget(self.spbTotal, 0, 2, 1, 1)
self.label_3 = QtWidgets.QLabel(self.groupBox_11)
self.label_3.setObjectName("label_3")
self.gridLayout.addWidget(self.label_3, 0, 3, 1, 1)
self.lneOutPath = QtWidgets.QLineEdit(self.groupBox_11)
self.lneOutPath.setObjectName("lneOutPath")
self.gridLayout.addWidget(self.lneOutPath, 0, 6, 1, 1)
self.lneTitle = QtWidgets.QLineEdit(self.groupBox_11)
self.lneTitle.setMinimumSize(QtCore.QSize(0, 22))
self.lneTitle.setObjectName("lneTitle")
self.gridLayout.addWidget(self.lneTitle, 1, 1, 1, 3)
self.label_2 = QtWidgets.QLabel(self.groupBox_11)
self.label_2.setObjectName("label_2")
self.gridLayout.addWidget(self.label_2, 0, 0, 1, 2)
self.label_5 = QtWidgets.QLabel(self.groupBox_11)
self.label_5.setObjectName("label_5")
self.gridLayout.addWidget(self.label_5, 1, 4, 1, 1)
self.label_6 = QtWidgets.QLabel(self.groupBox_11)
self.label_6.setObjectName("label_6")
self.gridLayout.addWidget(self.label_6, 0, 5, 1, 1)
self.label_4 = QtWidgets.QLabel(self.groupBox_11)
self.label_4.setObjectName("label_4")
self.gridLayout.addWidget(self.label_4, 1, 0, 1, 1)
self.verticalLayout.addWidget(self.groupBox_11)
self.btnGen = QtWidgets.QPushButton(MainWin)
self.btnGen.setMinimumSize(QtCore.QSize(0, 35))
self.btnGen.setObjectName("btnGen")
self.verticalLayout.addWidget(self.btnGen)
self.retranslateUi(MainWin)
QtCore.QMetaObject.connectSlotsByName(MainWin)
def retranslateUi(self, MainWin):
_translate = QtCore.QCoreApplication.translate
MainWin.setWindowTitle(_translate("MainWin", "MainWin"))
self.groupBox.setTitle(_translate("MainWin", "题型选择"))
self.gbxOpType.setTitle(_translate("MainWin", "运算类型选择"))
self.rabAdd.setText(_translate("MainWin", "加法"))
self.rabSub.setText(_translate("MainWin", "减法"))
self.rabMult.setText(_translate("MainWin", "乘法"))
self.rabDiv.setText(_translate("MainWin", "除法"))
self.gbxOpStep.setTitle(_translate("MainWin", "几步运算"))
self.rabOneStep.setText(_translate("MainWin", "一步"))
self.rabTwoStep.setText(_translate("MainWin", "二步"))
self.ranTreeStep.setText(_translate("MainWin", "三步"))
self.gbxSubjectType.setTitle(_translate("MainWin", "题目类型"))
self.rabResult.setText(_translate("MainWin", "求结果"))
self.rabItem.setText(_translate("MainWin", "求算数项"))
self.groupBox_5.setTitle(_translate("MainWin", "详细设置"))
self.groupBox_6.setTitle(_translate("MainWin", "运算项结果符合设置"))
self.btnOpResSet.setText(_translate("MainWin", "运算项及结果范围设置"))
self.btnOperatorSet.setText(_translate("MainWin", "运算符号设置"))
self.ckbBracket.setText(_translate("MainWin", "使用括号"))
self.gbxAddSet.setTitle(_translate("MainWin", "加法设置"))
self.rabRandCarry.setText(_translate("MainWin", "随机进位"))
self.rabAddCarry.setText(_translate("MainWin", "加法进位"))
self.rabNoCarry.setText(_translate("MainWin", "没有进位"))
self.gbxSubSet.setTitle(_translate("MainWin", "减法设置"))
self.rabRandAbdicate.setText(_translate("MainWin", "随机退位"))
self.rabSubAbdicate.setText(_translate("MainWin", "减法退位"))
self.rabNoAbdicate.setText(_translate("MainWin", "没有退位"))
self.groupBox_9.setTitle(_translate("MainWin", "添加计算题到试卷"))
self.label.setText(_translate("MainWin", "题目个数："))
self.btnAddSubject.setText(_translate("MainWin", "添加题目"))
self.btnClearSubject.setText(_translate("MainWin", "清空题目"))
self.groupBox_10.setTitle(_translate("MainWin", "当前试卷包含题目："))
self.groupBox_11.setTitle(_translate("MainWin", "试卷设置"))
self.btnBrowse.setText(_translate("MainWin", "浏览"))
self.label_3.setText(_translate("MainWin", "试卷列量："))
self.label_2.setText(_translate("MainWin", "生成试卷数量："))
self.label_5.setText(_translate("MainWin", "试卷副标题："))
self.label_6.setText(_translate("MainWin", "输出目录："))
self.label_4.setText(_translate("MainWin", "试卷标题："))
self.btnGen.setText(_translate("MainWin", "开始生成试卷"))
|
from typing import Sequence, Iterable, List
from KafNafParserPy import KafNafParser, Cterm, Cwf
def sort_tokens(tokens: Iterable[Cwf]) -> List[Cwf]:
"""Sort tokens by natural order (sent, offset)"""
return sorted(tokens, key=lambda t: (t.get_sent(), int(t.get_offset())))
def sort_terms(naf: KafNafParser, terms: Iterable[Cterm]) -> List[Cterm]:
"""Sort terms by natural order (sent, offset)"""
def get_offset(term: Cterm):
tokens = [naf.get_token(tid) for tid in naf.get_dict_tokens_for_termid(term.get_id())]
token = sort_tokens(tokens).pop()
return token.get_sent(), int(token.get_offset())
return sorted(terms, key=get_offset)
def get_word(naf: KafNafParser, term: Cterm) -> str:
"""Get the word(s) belonging to a term, joining them if there's more than one"""
tokenids = naf.get_dict_tokens_for_termid(term.get_id())
tokens = sort_tokens(naf.get_token(tid) for tid in tokenids)
return " ".join(t.get_text() for t in tokens)
def find_terms(naf: KafNafParser, words: Sequence[str]) -> Iterable[Cterm]:
"""Find all terms whose lemma or word form is in the list of words"""
for t in naf.get_terms():
if t.get_lemma() in words or get_word(naf, t) in words:
yield t
def get_sentence(naf: KafNafParser, term: Cterm) -> int:
tokens = [naf.get_token(tid) for tid in naf.get_dict_tokens_for_termid(term.get_id())]
sent = {t.get_sent() for t in tokens}
if len(sent) != 1:
raise Exception(f"Term {term.get_id}:{term.get_lemma()} did not map to single sentence: {sent}")
return sent.pop()
def get_terms_in_sentence(naf: KafNafParser, sent: int) -> Iterable[Cterm]:
tokens = sort_tokens(t for t in naf.get_tokens() if t.get_sent() == sent)
tokenids = [t.get_id() for t in tokens]
return sort_terms(naf, [naf.get_term(tid) for tid in naf.map_tokens_to_terms(tokenids)]) |
transform_table = bytes.fromhex("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")
target = [i%256 for i in [-74, 56, -99, -111, 95, 98, -38, -116, -5, 76, -18, -84, -65, -112, 31, -81]]
b2 = 0
flag = bytearray(b'a'*16)
for i in range(0,len(target),2):
b1 = transform_table[i]
flag[i] = transform_table.index(target[i] ^ b1 ^ b2)
b2 = transform_table[i+1] ^ b1 ^ b2
flag[i+1] = transform_table.index(target[i+1] ^ b2)
print(flag) |
import os
import logging
import time
from azureml.core.authentication import ServicePrincipalAuthentication
_TENANT_ID_ENV_NAME = "TenantId"
_SERVICE_PRINCIPAL_ID_ENV_NAME = "ServicePrincipalId"
_SERVICE_PRINCIPAL_SECRET_ENV_NAME = "ServicePrincipalSecret"
def get_service_principal_auth():
tenant_id = os.environ[_TENANT_ID_ENV_NAME]
service_principal_id = os.environ[_SERVICE_PRINCIPAL_ID_ENV_NAME]
service_principal_password = os.environ[_SERVICE_PRINCIPAL_SECRET_ENV_NAME]
svc_pr = ServicePrincipalAuthentication(
tenant_id=tenant_id,
service_principal_id=service_principal_id,
service_principal_password=service_principal_password)
return svc_pr
def get_access_token():
start_time = time.time()
svc_pr = get_service_principal_auth()
aad_token = svc_pr.get_authentication_header()
end_time = time.time()
logging.info('Get Access Token Time: %s seconds', end_time - start_time)
return aad_token
|
"""
214. Shortest Palindrome
Given a string s, you are allowed to convert it to a palindrome by adding characters in front of it.
Find and return the shortest palindrome you can find by performing this transformation.
Example 1:
Input: "aacecaaa"
Output: "aaacecaaa"
Example 2:
Input: "abcd"
Output: "dcbabcd"
"""
class Solution:
def shortestPalindrome(self, s):
"""
:type s: str
:rtype: str
"""
snew = s + "#" +s[::-1]
def getPrefix(snew):
prefix = [0]*len(snew)
j = 0
for i in range(1,len(snew)):
while j > 0 and snew[i]!=snew[j]:
j = prefix[j-1]
if snew[i] == snew[j]: j+=1
prefix[i] = j
return prefix
kmp = getPrefix(snew)
nonpal = s[kmp[-1]:]
return nonpal[::-1] + s
import functools
class Solution:
def shortestPalindrome(self, s):
snew = functools.reduce(lambda x, y: x + y + "#", s,"$#")+"^"
def manacher(snew):
p = [0]*len(snew)
mx = id = maxlen = 0
for i in range(1,len(snew)-1):
if i < mx:
p[i] = min(p[id*2 - i], p[mx - i])
else:
p[i] = 1
while snew[i + p[i]] == snew[i - p[i]]:
p[i] += 1
if p[i] + i > mx:
id, mx = i, p[i]+i
if p[i] == i:
maxlen = max(maxlen, p[i]-1)
return maxlen
maxlen = manacher(snew)
nonpal = s[maxlen:]
return nonpal[::-1] + s
"""
The basic idea is to find the longest palindrome starting from s[0], so that fewest charactors are needed in front of s.
For any charactor(c) in s appearing more than once, define l and r as the first and last index of c,
then the max length of palindrome starting from s[0] would be no larger than l+r+1, or the first c could never be matched.
For any charactor(c) in s appearing just once, l=r. Here is another key optimization.if s[:l+r+1] is not a palindrome,
the max length of palindrome starting from s[0] would be no larger than l.
In other words, c must be excluded from the palindrome, or it could not be matched.
If s[:l+r+1] is a palindrome, actually c is the center, matched by itself.
"""
class Solution:
def shortestPalindrome(self, s):
"""
:type s: str
:rtype: str
"""
if not s: return ''
k=len(s)
for c in set(s):
l,r=s.find(c),s.rfind(c)
k=min(k,l if l==r and s[:l+r+1]!=s[:l+r+1][::-1] else l+r+1)
for i in range(k,0,-1):
if s[:i]==s[:i][::-1]: return s[i:][::-1]+s
|
#!/usr/bin/env python
import argparse, yaml
from xidb import Guild
parser = argparse.ArgumentParser(description="Generate project xid")
parser.add_argument('-c', '--config', dest='config', required=True)
args = parser.parse_args()
with open(args.config) as f:
config = yaml.load(f.read())
guild = Guild(config)
print "guild project", guild.guildProject.xid
print "wiki project", guild.wikiProject.xid
print "viki project", guild.projProject.xid
|
import argparse
import logging
from role_analyzer import allows
import yaml
from z3 import Distinct, Solver, sat, unsat # type: ignore
def roles_are_equivalent(r1, r2) -> tuple[bool, str]:
r1 = allows(r1)
r2 = allows(r2)
s = Solver()
s.add(Distinct(r1, r2))
result = s.check()
if unsat == result:
return (True, 'Roles are equivalent')
elif sat == result:
return (False, f'Roles are not equivalent; counterexample: {s.model()}')
else:
return (False, str(result))
def main():
parser = argparse.ArgumentParser(description='Check two roles for equivalence.')
parser.add_argument('first', metavar='FIRST', type=str, help='Path to the first role\'s yaml file')
parser.add_argument('second', metavar='SECOND', type=str, help='Path to the second role\'s yaml file')
parser.add_argument('--debug', dest='log_level', action='store_const', const=logging.DEBUG, default=logging.INFO, help='Print Z3 translation debug output')
args = parser.parse_args()
logging.basicConfig(level=args.log_level)
with (
open(args.first, 'r') as r1,
open(args.second, 'r') as r2
):
try:
r1 = yaml.safe_load(r1)
r2 = yaml.safe_load(r2)
are_equivalent, msg = roles_are_equivalent(r1, r2)
print(msg)
#exit(0 if are_equivalent else 1)
except yaml.YAMLError as e:
print(e)
if __name__ == '__main__':
main() |
#!/usr/bin/env python3
import unittest
class Fence:
def __init__(self, woods):
self.__woods = woods
self.size = len(woods)
self.__init_db()
def __init_db(self):
self.__left_db = self.__init_db_to_left()
self.__right_db = self.__init_db_to_right()
def height(self, i):
if i==-1:
return 0
elif i==self.size:
return 0
else:
return self.__woods[i]
def __init_db_to_left(self):
db = [-1]
for i,h in enumerate(self.__woods[1:], 1):
if self.height(i-1) < h:
db.append(i-1)
else:
idx = i-1
while self.height(idx) >= h:
idx = db[idx]
db.append(idx)
return db
def __init_db_to_right(self):
db = [None]*(self.size-1) + [self.size]
for i in range(self.size-2, -1, -1):
h = self.height(i)
if h > self.height(i+1):
db[i] = i+1
else:
idx = i+1
while h <= self.height(idx):
idx = db[idx]
db[i]=(idx)
return db
def left(self, i):
return self.__left_db[i]
def right(self, i):
return self.__right_db[i]
def get_max(self):
res = 0
for i,height in enumerate(self.__woods):
width = self.right(i) - self.left(i) - 1
area = height * width
res = max(area, res)
return res
class FenceTest(unittest.TestCase):
def test_db_left(self):
f = Fence([3,2,1])
self.assertEqual([f.left(i) for i in [0,1,2]], [-1, -1, -1])
f = Fence([1,2,3])
self.assertEqual([f.left(i) for i in [0,1,2]], [-1, 0, 1])
f = Fence([1,3,2])
self.assertEqual([f.left(i) for i in [0,1,2]], [-1, 0, 0])
def test_db_right(self):
f = Fence([3,2,1])
self.assertEqual([f.right(i) for i in [2,1,0]], [3,2,1])
f = Fence([1,2,3])
self.assertEqual([f.right(i) for i in [2,1,0]], [3, 3, 3])
f = Fence([1,3,2])
self.assertEqual([f.right(i) for i in [2,1,0]], [3, 2, 3])
def assertFence(self, woods, maxsum):
f = Fence(woods)
self.assertEqual(f.get_max(), maxsum)
def test_samples(self):
self.assertFence(woods=[7,1,5,9,6,7,3], maxsum=20)
self.assertFence(woods=[1,4,4,4,4,1,1], maxsum=16)
self.assertFence(woods=[1,8,2,2], maxsum=8)
def test_if_this_takes_O_of_n(self):
from time import time
for x in [10000, 50000, 250000]:
woods = self.generate_woods(x)
start = time()
Fence(woods).get_max()
execution_time = time() - start
print(x, ':', execution_time)
''' YES! it's O(n) as I expected!
10000 : 0.02214670181274414
50000 : 0.0985422134399414
250000 : 0.49942612648010254
'''
def generate_woods(self, x):
''' return x-length of a list of natural numbers [1,10000]'''
from random import randint
return [randint(1,10000) for _ in range(x)]
if __name__=="__main__":
unittest.main()
|
from piece import Piece
from util import pattern, select, rep, join
from tones import tonify
from points import note, notes, chord, rest, tied_note
from markup import voices
class PreludeInCSimple(Piece):
def details(self):
self.title = "Prelude in C"
self.composer = "J. S. Bach"
self.opus = "BVW 846"
def motif(self, c):
tones = tonify(c)
return {
'treble': rep(rest(8) + notes(pattern(tones, 2 * [3, 4, 5]), 16), 2),
'bass': rep(voices(rest(16) + tied_note(select(tones, 2), ['8.', 4]), note(select(tones, 1), 2)), 2)
}
@property
def chords(self):
bar = [''] * 40
bar[1] = 'c` e` g` c`` e``'
bar[2] = 'c` d` g` c`` e``'
bar[3] = 'b d` g` d`` f``'
bar[4] = 'c` e` g` c`` e``'
bar[5] = 'c` e` a` e`` a``'
bar[6] = 'c` d` df` a` d``'
bar[7] = 'b d` g` d`` g``'
bar[8] = 'b c` e` g` c``'
bar[9] = 'a c` e` g` c``'
bar[10] = 'd a d` fs` c``'
bar[11] = 'g b d` g` b`'
bar[12] = 'g bf e` g` cs``'
bar[13] = 'f a d` a` d``'
bar[14] = 'f af d` f` b`'
bar[15] = 'e g c` g` c``'
bar[16] = 'e f a c` f`'
bar[17] = 'd f a c` f`'
bar[18] = 'g, d g b f`'
bar[19] = 'c e g c` e`'
bar[20] = 'c g bf c` e`'
bar[21] = 'f, f a c` e`'
bar[22] = 'fs, c a c` ef`'
bar[23] = 'af, f b c` d`'
bar[24] = 'g, f g b d`'
bar[25] = 'g, e g c` e`'
bar[26] = 'g, d g c` f`'
bar[27] = 'g, d g b f`'
bar[28] = 'g, ef a c` fs`'
bar[29] = 'g, e g c` g`'
bar[30] = 'g, d g c` f`'
bar[31] = 'g, d g b f`'
bar[32] = 'c, c g bf e`'
return bar
def held_bass(self, tones):
tones = tonify(tones)
return voices(rest(16) + tied_note(tones[1], ['8.', 4, 2]), note(tones[0], 1))
def long_melody(self, tones):
tones = tonify(tones)
return rest(8) + notes(pattern(tones, 1, 2, 3, 4, 3, 2, 3, 2, 1, 2), 16)
@property
def outro(self):
return {
'treble': self.long_melody('f a c` f`') + notes('f d', 16) * 2 + self.long_melody('g` b` d`` f``') + pattern(self.scale('d`', 'f`', 16), 1, 3, 2, 1) + chord('e` g` c`', 1),
'bass': self.held_bass('c, c') + self.held_bass('c, b,') + chord('c, c', 1)
}
def write_score(self):
self.score = join([self.motif(chord) for chord in self.chords[1:33]])
self.score = join(self.score, self.outro)
if __name__ == "__main__":
PreludeInCSimple()
|
# -*- coding: utf-8 -*-
# Generated by Django 1.11.5 on 2017-09-12 09:00
from __future__ import unicode_literals
from django.db import migrations, models
class Migration(migrations.Migration):
dependencies = [
('fpraktikum', '0010_auto_20170910_1434'),
]
operations = [
migrations.CreateModel(
name='UsrData',
fields=[
('usr_id', models.IntegerField(primary_key=True, serialize=False)),
('login', models.CharField(blank=True, max_length=80, null=True, unique=True)),
('passwd', models.CharField(blank=True, max_length=80, null=True)),
('firstname', models.CharField(blank=True, max_length=32, null=True)),
('lastname', models.CharField(blank=True, max_length=32, null=True)),
('title', models.CharField(blank=True, max_length=32, null=True)),
('gender', models.CharField(blank=True, max_length=1, null=True)),
('email', models.CharField(blank=True, max_length=80, null=True)),
('institution', models.CharField(blank=True, max_length=80, null=True)),
('street', models.CharField(blank=True, max_length=40, null=True)),
('city', models.CharField(blank=True, max_length=40, null=True)),
('zipcode', models.CharField(blank=True, max_length=10, null=True)),
('country', models.CharField(blank=True, max_length=40, null=True)),
('phone_office', models.CharField(blank=True, max_length=40, null=True)),
('last_login', models.DateTimeField(blank=True, null=True)),
('last_update', models.DateTimeField(blank=True, null=True)),
('create_date', models.DateTimeField(blank=True, null=True)),
('hobby', models.CharField(blank=True, max_length=4000, null=True)),
('department', models.CharField(blank=True, max_length=80, null=True)),
('phone_home', models.CharField(blank=True, max_length=40, null=True)),
('phone_mobile', models.CharField(blank=True, max_length=40, null=True)),
('fax', models.CharField(blank=True, max_length=40, null=True)),
('time_limit_owner', models.IntegerField(blank=True, null=True)),
('time_limit_unlimited', models.IntegerField(blank=True, null=True)),
('time_limit_from', models.IntegerField(blank=True, null=True)),
('time_limit_until', models.IntegerField(blank=True, null=True)),
('time_limit_message', models.IntegerField(blank=True, null=True)),
('referral_comment', models.CharField(blank=True, max_length=250, null=True)),
('matriculation', models.CharField(blank=True, max_length=40, null=True)),
('active', models.IntegerField()),
('approve_date', models.DateTimeField(blank=True, null=True)),
('agree_date', models.DateTimeField(blank=True, null=True)),
('client_ip', models.CharField(blank=True, max_length=255, null=True)),
('auth_mode', models.CharField(blank=True, max_length=10, null=True)),
('profile_incomplete', models.IntegerField(blank=True, null=True)),
('ext_account', models.CharField(blank=True, max_length=250, null=True)),
('im_icq', models.CharField(blank=True, max_length=40, null=True)),
('im_yahoo', models.CharField(blank=True, max_length=40, null=True)),
('im_msn', models.CharField(blank=True, max_length=40, null=True)),
('im_aim', models.CharField(blank=True, max_length=40, null=True)),
('im_skype', models.CharField(blank=True, max_length=40, null=True)),
('feed_hash', models.CharField(blank=True, max_length=32, null=True)),
('delicious', models.CharField(blank=True, max_length=40, null=True)),
('latitude', models.CharField(blank=True, max_length=30, null=True)),
('longitude', models.CharField(blank=True, max_length=30, null=True)),
('loc_zoom', models.IntegerField()),
('login_attempts', models.IntegerField()),
('last_password_change', models.IntegerField()),
('im_jabber', models.CharField(blank=True, max_length=40, null=True)),
('im_voip', models.CharField(blank=True, max_length=40, null=True)),
('reg_hash', models.CharField(blank=True, max_length=32, null=True)),
('birthday', models.DateField(blank=True, null=True)),
('sel_country', models.CharField(blank=True, max_length=2, null=True)),
('last_visited', models.TextField(blank=True, null=True)),
('inactivation_date', models.DateTimeField(blank=True, null=True)),
('is_self_registered', models.IntegerField()),
('passwd_enc_type', models.CharField(blank=True, max_length=10, null=True)),
('passwd_salt', models.CharField(blank=True, max_length=32, null=True)),
],
options={
'db_table': 'usr_data',
'managed': False,
},
),
migrations.RenameField(
model_name='fpuserpartner',
old_name='user_snumber',
new_name='user_login',
),
migrations.RenameField(
model_name='fpuserregistrant',
old_name='user_snumber',
new_name='user_login',
),
migrations.AlterField(
model_name='fpinstitute',
name='places',
field=models.IntegerField(blank=True, default=0, null=True, verbose_name='places'),
),
]
|
# compatibility with deprecated API
from nuclear.shell.shell_utils import shell, shell_error_code, shell_output
|
from operator import attrgetter
import pyangbind.lib.xpathhelper as xpathhelper
from pyangbind.lib.yangtypes import RestrictedPrecisionDecimalType, RestrictedClassType, TypedListType
from pyangbind.lib.yangtypes import YANGBool, YANGListType, YANGDynClass, ReferenceType
from pyangbind.lib.base import PybindBase
from decimal import Decimal
from bitarray import bitarray
import __builtin__
import fwdl_status
import activate_status
import firmware_download
import dad_status
class brocade_firmware(PybindBase):
"""
This class was auto-generated by the PythonClass plugin for PYANG
from YANG module brocade-firmware - based on the path /brocade_firmware_rpc. Each member element of
the container is represented as a class variable - with a specific
YANG type.
YANG Description: This management module is an instrumentation to firmware level
level commands
"""
__slots__ = ('_pybind_generated_by', '_path_helper', '_yang_name', '_rest_name', '_extmethods', '__fwdl_status','__activate_status','__firmware_download','__dad_status',)
_yang_name = 'brocade-firmware'
_rest_name = ''
_pybind_generated_by = 'container'
def __init__(self, *args, **kwargs):
path_helper_ = kwargs.pop("path_helper", None)
if path_helper_ is False:
self._path_helper = False
elif path_helper_ is not None and isinstance(path_helper_, xpathhelper.YANGPathHelper):
self._path_helper = path_helper_
elif hasattr(self, "_parent"):
path_helper_ = getattr(self._parent, "_path_helper", False)
self._path_helper = path_helper_
else:
self._path_helper = False
extmethods = kwargs.pop("extmethods", None)
if extmethods is False:
self._extmethods = False
elif extmethods is not None and isinstance(extmethods, dict):
self._extmethods = extmethods
elif hasattr(self, "_parent"):
extmethods = getattr(self._parent, "_extmethods", None)
self._extmethods = extmethods
else:
self._extmethods = False
self.__activate_status = YANGDynClass(base=activate_status.activate_status, is_leaf=True, yang_name="activate-status", rest_name="activate-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Retrieve firmware activation status.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
self.__fwdl_status = YANGDynClass(base=fwdl_status.fwdl_status, is_leaf=True, yang_name="fwdl-status", rest_name="fwdl-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display firmware download status for the specified node', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
self.__dad_status = YANGDynClass(base=dad_status.dad_status, is_leaf=True, yang_name="dad-status", rest_name="dad-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display DHCP auto-deployment status', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
self.__firmware_download = YANGDynClass(base=firmware_download.firmware_download, is_leaf=True, yang_name="firmware-download", rest_name="firmware-download", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'To perfrom the firmware download.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
load = kwargs.pop("load", None)
if args:
if len(args) > 1:
raise TypeError("cannot create a YANG container with >1 argument")
all_attr = True
for e in self._pyangbind_elements:
if not hasattr(args[0], e):
all_attr = False
break
if not all_attr:
raise ValueError("Supplied object did not have the correct attributes")
for e in self._pyangbind_elements:
nobj = getattr(args[0], e)
if nobj._changed() is False:
continue
setmethod = getattr(self, "_set_%s" % e)
if load is None:
setmethod(getattr(args[0], e))
else:
setmethod(getattr(args[0], e), load=load)
def _path(self):
if hasattr(self, "_parent"):
return self._parent._path()+[self._yang_name]
else:
return [u'brocade_firmware_rpc']
def _rest_path(self):
if hasattr(self, "_parent"):
if self._rest_name:
return self._parent._rest_path()+[self._rest_name]
else:
return self._parent._rest_path()
else:
return []
def _get_fwdl_status(self):
"""
Getter method for fwdl_status, mapped from YANG variable /brocade_firmware_rpc/fwdl_status (rpc)
"""
return self.__fwdl_status
def _set_fwdl_status(self, v, load=False):
"""
Setter method for fwdl_status, mapped from YANG variable /brocade_firmware_rpc/fwdl_status (rpc)
If this variable is read-only (config: false) in the
source YANG file, then _set_fwdl_status is considered as a private
method. Backends looking to populate this variable should
do so via calling thisObj._set_fwdl_status() directly.
"""
if hasattr(v, "_utype"):
v = v._utype(v)
try:
t = YANGDynClass(v,base=fwdl_status.fwdl_status, is_leaf=True, yang_name="fwdl-status", rest_name="fwdl-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display firmware download status for the specified node', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
except (TypeError, ValueError):
raise ValueError({
'error-string': """fwdl_status must be of a type compatible with rpc""",
'defined-type': "rpc",
'generated-type': """YANGDynClass(base=fwdl_status.fwdl_status, is_leaf=True, yang_name="fwdl-status", rest_name="fwdl-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display firmware download status for the specified node', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)""",
})
self.__fwdl_status = t
if hasattr(self, '_set'):
self._set()
def _unset_fwdl_status(self):
self.__fwdl_status = YANGDynClass(base=fwdl_status.fwdl_status, is_leaf=True, yang_name="fwdl-status", rest_name="fwdl-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display firmware download status for the specified node', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
def _get_activate_status(self):
"""
Getter method for activate_status, mapped from YANG variable /brocade_firmware_rpc/activate_status (rpc)
"""
return self.__activate_status
def _set_activate_status(self, v, load=False):
"""
Setter method for activate_status, mapped from YANG variable /brocade_firmware_rpc/activate_status (rpc)
If this variable is read-only (config: false) in the
source YANG file, then _set_activate_status is considered as a private
method. Backends looking to populate this variable should
do so via calling thisObj._set_activate_status() directly.
"""
if hasattr(v, "_utype"):
v = v._utype(v)
try:
t = YANGDynClass(v,base=activate_status.activate_status, is_leaf=True, yang_name="activate-status", rest_name="activate-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Retrieve firmware activation status.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
except (TypeError, ValueError):
raise ValueError({
'error-string': """activate_status must be of a type compatible with rpc""",
'defined-type': "rpc",
'generated-type': """YANGDynClass(base=activate_status.activate_status, is_leaf=True, yang_name="activate-status", rest_name="activate-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Retrieve firmware activation status.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)""",
})
self.__activate_status = t
if hasattr(self, '_set'):
self._set()
def _unset_activate_status(self):
self.__activate_status = YANGDynClass(base=activate_status.activate_status, is_leaf=True, yang_name="activate-status", rest_name="activate-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Retrieve firmware activation status.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
def _get_firmware_download(self):
"""
Getter method for firmware_download, mapped from YANG variable /brocade_firmware_rpc/firmware_download (rpc)
"""
return self.__firmware_download
def _set_firmware_download(self, v, load=False):
"""
Setter method for firmware_download, mapped from YANG variable /brocade_firmware_rpc/firmware_download (rpc)
If this variable is read-only (config: false) in the
source YANG file, then _set_firmware_download is considered as a private
method. Backends looking to populate this variable should
do so via calling thisObj._set_firmware_download() directly.
"""
if hasattr(v, "_utype"):
v = v._utype(v)
try:
t = YANGDynClass(v,base=firmware_download.firmware_download, is_leaf=True, yang_name="firmware-download", rest_name="firmware-download", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'To perfrom the firmware download.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
except (TypeError, ValueError):
raise ValueError({
'error-string': """firmware_download must be of a type compatible with rpc""",
'defined-type': "rpc",
'generated-type': """YANGDynClass(base=firmware_download.firmware_download, is_leaf=True, yang_name="firmware-download", rest_name="firmware-download", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'To perfrom the firmware download.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)""",
})
self.__firmware_download = t
if hasattr(self, '_set'):
self._set()
def _unset_firmware_download(self):
self.__firmware_download = YANGDynClass(base=firmware_download.firmware_download, is_leaf=True, yang_name="firmware-download", rest_name="firmware-download", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'To perfrom the firmware download.', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
def _get_dad_status(self):
"""
Getter method for dad_status, mapped from YANG variable /brocade_firmware_rpc/dad_status (rpc)
"""
return self.__dad_status
def _set_dad_status(self, v, load=False):
"""
Setter method for dad_status, mapped from YANG variable /brocade_firmware_rpc/dad_status (rpc)
If this variable is read-only (config: false) in the
source YANG file, then _set_dad_status is considered as a private
method. Backends looking to populate this variable should
do so via calling thisObj._set_dad_status() directly.
"""
if hasattr(v, "_utype"):
v = v._utype(v)
try:
t = YANGDynClass(v,base=dad_status.dad_status, is_leaf=True, yang_name="dad-status", rest_name="dad-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display DHCP auto-deployment status', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
except (TypeError, ValueError):
raise ValueError({
'error-string': """dad_status must be of a type compatible with rpc""",
'defined-type': "rpc",
'generated-type': """YANGDynClass(base=dad_status.dad_status, is_leaf=True, yang_name="dad-status", rest_name="dad-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display DHCP auto-deployment status', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)""",
})
self.__dad_status = t
if hasattr(self, '_set'):
self._set()
def _unset_dad_status(self):
self.__dad_status = YANGDynClass(base=dad_status.dad_status, is_leaf=True, yang_name="dad-status", rest_name="dad-status", parent=self, path_helper=self._path_helper, extmethods=self._extmethods, register_paths=False, extensions={u'tailf-common': {u'info': u'Display DHCP auto-deployment status', u'hidden': u'rpccmd', u'actionpoint': u'firmware'}}, namespace='urn:brocade.com:mgmt:brocade-firmware', defining_module='brocade-firmware', yang_type='rpc', is_config=True)
fwdl_status = __builtin__.property(_get_fwdl_status, _set_fwdl_status)
activate_status = __builtin__.property(_get_activate_status, _set_activate_status)
firmware_download = __builtin__.property(_get_firmware_download, _set_firmware_download)
dad_status = __builtin__.property(_get_dad_status, _set_dad_status)
_pyangbind_elements = {'fwdl_status': fwdl_status, 'activate_status': activate_status, 'firmware_download': firmware_download, 'dad_status': dad_status, }
|
# Copyright 2013 Mirantis, Inc.
#
# Licensed under the Apache License, Version 2.0 (the "License"); you may
# not use this file except in compliance with the License. You may obtain
# a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
# WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
# License for the specific language governing permissions and limitations
# under the License.
from nailgun.db.sqlalchemy.models import Cluster
from nailgun.db.sqlalchemy.models import NetworkGroup
from nailgun.db.sqlalchemy.models import node
from nailgun.errors import errors
from nailgun.network.checker import NetworkCheck
from nailgun.task import helpers
from nailgun.test.base import BaseIntegrationTest
from mock import MagicMock
from mock import patch
class FakeTask(object):
def __init__(self, cluster):
self.cluster = cluster
class TestNetworkCheck(BaseIntegrationTest):
def setUp(self):
super(TestNetworkCheck, self).setUp()
self.env.create(
cluster_kwargs={},
nodes_kwargs=[
{"api": True,
"pending_addition": True},
]
)
self.task = FakeTask(self.env.clusters[0])
@patch.object(helpers, 'db')
def test_check_untagged_intersection_failed(self, mocked_db):
cluster = self.env.create(
nodes_kwargs=[
{'roles': ['controller'], 'pending_addition': True}
]
)
cluster_db = self.db.query(Cluster).get(cluster['id'])
checker = NetworkCheck(FakeTask(cluster_db), {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'fake1',
'vlan_start': None,
'meta': {'notation': 'cidr'}},
{'id': 2,
'cidr': '192.168.0.0/26',
'name': 'fake2',
'vlan_start': None,
'meta': {'notation': 'cidr'}}]
ng1 = NetworkGroup()
ng1.name = 'fake1'
ng1.id = 1
ng2 = NetworkGroup()
ng2.name = 'fake2'
ng2.id = 2
checker.cluster.nodes[0].interfaces[0].assigned_networks_list = \
[ng1, ng2]
checker.cluster.nodes[0].interfaces[1].assigned_networks_list = \
[ng1, ng2]
self.assertRaises(errors.NetworkCheckError,
checker.check_untagged_intersection)
def test_check_untagged_intersection(self):
cluster = self.env.create(
nodes_kwargs=[
{'roles': ['controller'], 'pending_addition': True}
]
)
cluster_db = self.db.query(Cluster).get(cluster['id'])
checker = NetworkCheck(FakeTask(cluster_db), {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'fake1',
'vlan_start': None,
'meta': {'notation': 'cidr'}}]
ng1 = NetworkGroup()
ng1.name = 'fake3'
ng1.id = 3
ng2 = NetworkGroup()
ng2.name = 'fake4'
ng2.id = 4
checker.cluster.nodes[0].interfaces[0].assigned_networks_list = \
[ng1, ng2]
self.assertNotRaises(errors.NetworkCheckError,
checker.check_untagged_intersection)
@patch.object(helpers, 'db')
def test_check_network_address_spaces_intersection(self, mocked_db):
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'fake1',
'meta': {'notation': 'cidr'}},
{'id': 2,
'cidr': '192.168.0.0/26',
'name': 'fake2',
'meta': {'notation': 'cidr'}}]
self.assertRaises(errors.NetworkCheckError,
checker.check_network_address_spaces_intersection)
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'fake1',
'meta': {'notation': 'cidr'}},
{'id': 2,
'cidr': '192.168.1.0/26',
'name': 'fake2',
'meta': {'notation': 'cidr'}}]
checker.network_config['fixed_networks_cidr'] = '10.20.0.0/24'
self.assertNotRaises(errors.NetworkCheckError,
checker.check_network_address_spaces_intersection)
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'fake1',
'meta': {'notation': 'cidr'}},
{'id': 2,
'cidr': '10.20.0.0/26',
'name': 'fake2',
'meta': {'notation': 'cidr'}}]
checker.network_config['fixed_networks_cidr'] = '10.20.0.0/24'
self.assertRaises(errors.NetworkCheckError,
checker.check_network_address_spaces_intersection)
@patch.object(helpers, 'db')
def test_check_public_floating_ranges_intersection(self, mocked_db):
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'public',
'gateway': '192.168.0.1',
'ip_ranges': ['192.168.0.1', '192.168.0.100'],
'meta': {'notation': 'cidr'}}]
checker.network_config['floating_ranges'] = ['192.168.0.100',
'192.168.0.199']
self.assertRaises(errors.NetworkCheckError,
checker.check_public_floating_ranges_intersection)
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'public',
'gateway': '192.168.0.1',
'ip_ranges': [('192.168.0.1', '192.168.0.254')],
'meta': {'notation': 'cidr'}}]
checker.network_config['floating_ranges'] = ['192.168.2.0/24']
self.assertRaises(errors.NetworkCheckError,
checker.check_public_floating_ranges_intersection)
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'public',
'gateway': '192.168.0.1',
'ip_ranges': [('192.168.0.2', '192.168.0.254')],
'meta': {'notation': 'cidr'}}]
checker.network_config['floating_ranges'] = ['192.168.2.0/24']
self.assertNotRaises(errors.NetworkCheckError,
checker.check_public_floating_ranges_intersection)
@patch.object(helpers, 'db')
def test_check_vlan_ids_range_and_intersection_failed(self, mocked_db):
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'fixed',
'gateway': '192.168.0.1',
'vlan_start': 1}]
checker.network_config['fixed_networks_vlan_start'] = 1
checker.network_config['fixed_networks_amount'] = 10
self.assertRaises(errors.NetworkCheckError,
checker.check_vlan_ids_range_and_intersection)
@patch.object(helpers, 'db')
def test_check_vlan_ids_range_and_intersection(self, mocked_db):
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'name': 'fixed',
'gateway': '192.168.0.1',
'vlan_start': 200}]
checker.network_config['fixed_networks_vlan_start'] = 2
checker.network_config['fixed_networks_amount'] = 10
self.assertNotRaises(errors.NetworkCheckError,
checker.check_vlan_ids_range_and_intersection)
@patch.object(helpers, 'db')
def test_check_networks_amount(self, mocked_db):
checker = NetworkCheck(self.task, {})
checker.network_config['net_manager'] = 'FlatDHCPManager'
checker.network_config['fixed_networks_amount'] = 2
self.assertNotRaises(errors.NetworkCheckError,
checker.check_networks_amount)
checker = NetworkCheck(self.task, {})
checker.network_config['net_manager'] = 'FlatDHCPManager'
checker.network_config['fixed_networks_amount'] = 1
self.assertNotRaises(errors.NetworkCheckError,
checker.check_networks_amount)
checker = NetworkCheck(self.task, {})
checker.network_config['fixed_network_size'] = 100
checker.network_config['fixed_networks_amount'] = 3
checker.network_config['fixed_networks_cidr'] = '192.168.10.1/24'
self.assertNotRaises(errors.NetworkCheckError,
checker.check_networks_amount)
checker = NetworkCheck(self.task, {})
checker.network_config['fixed_network_size'] = 10
checker.network_config['fixed_networks_amount'] = 1
checker.network_config['fixed_networks_cidr'] = '192.168.10.1/24'
self.assertNotRaises(errors.NetworkCheckError,
checker.check_networks_amount)
@patch.object(helpers, 'db')
def test_neutron_check_l3_addresses_not_match_subnet_and_broadcast(
self, mocked_db):
checker = NetworkCheck(self.task, {})
checker.network_config['floating_ranges'] = [('192.168.0.1',
'192.168.0.255')]
checker.network_config['internal_cidr'] = '192.168.0.0/24'
checker.network_config['internal_gateway'] = '192.168.0.0'
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'gateway': '192.168.0.1',
'name': 'public'}]
self.assertRaises(
errors.NetworkCheckError,
checker.neutron_check_l3_addresses_not_match_subnet_and_broadcast)
self.assertEqual(len(checker.err_msgs), 2)
def test_check_network_classes_exclude_loopback(self):
checker = NetworkCheck(self.task, {})
checker.networks = [{'cidr': '192.168.0.0/24'}]
self.assertNotRaises(errors.NetworkCheckError,
checker.check_network_classes_exclude_loopback)
@patch.object(helpers, 'db')
def test_check_network_classes_exclude_loopback_fail(self, mocked_db):
checker = NetworkCheck(self.task, {})
networks = ['224.0.0.0/3', '127.0.0.0/8']
for network in networks:
checker.networks = [{'id': 1, 'cidr': network, 'name': 'fake'}]
self.assertRaises(errors.NetworkCheckError,
checker.check_network_classes_exclude_loopback)
self.assertEqual(mocked_db.call_count, 4)
@patch.object(helpers, 'db')
def test_check_network_addresses_not_match_subnet_and_broadcast(self,
mocked_db):
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'gateway': '192.168.0.1',
'name': 'fake1',
'meta': {'notation': 'ip_ranges'}}]
self.assertNotRaises(
errors.NetworkCheckError,
checker.check_network_addresses_not_match_subnet_and_broadcast)
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'gateway': '192.168.0.0',
'name': 'fake1',
'meta': {'notation': 'ip_ranges'}}]
self.assertRaises(
errors.NetworkCheckError,
checker.check_network_addresses_not_match_subnet_and_broadcast)
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'ip_ranges': ['192.168.0.1', '192.168.0.100'],
'gateway': '192.168.0.0',
'name': 'fake1',
'meta': {'notation': 'ip_ranges'}}]
self.assertRaises(
errors.NetworkCheckError,
checker.check_network_addresses_not_match_subnet_and_broadcast)
checker = NetworkCheck(self.task, {})
checker.networks = [{'id': 1,
'cidr': '192.168.0.0/24',
'ip_ranges': ['192.168.1.1', '192.168.1.100'],
'gateway': '192.168.0.1',
'name': 'fake1',
'meta': {'notation': 'ip_ranges'}}]
self.assertNotRaises(
errors.NetworkCheckError,
checker.check_network_addresses_not_match_subnet_and_broadcast)
def test_check_bond_slaves_speeds(self):
cluster = self.env.create(
nodes_kwargs=[
{'roles': ['controller'], 'pending_addition': True}
]
)
cluster_db = self.db.query(Cluster).get(cluster['id'])
checker = NetworkCheck(FakeTask(cluster_db), {})
checker.check_bond_slaves_speeds()
self.assertEqual(checker.err_msgs, [])
bond_if1 = node.NodeBondInterface()
bond_if2 = node.NodeBondInterface()
nic1 = node.NodeNICInterface()
nic2 = node.NodeNICInterface()
nic3 = node.NodeNICInterface()
nic1.current_speed = 100
nic2.current_speed = 10
nic3.current_speed = None
bond_if1.slaves = [nic1, nic2, nic3]
bond_if2.slaves = [nic3]
checker.cluster.nodes[0].bond_interfaces = [bond_if1, bond_if2]
checker.check_bond_slaves_speeds()
self.assertEqual(len(checker.err_msgs), 2)
def test_check_configuration_neutron(self):
checker = NetworkCheck(self.task, {})
checker.net_provider = 'neutron'
checker.neutron_check_network_address_spaces_intersection = MagicMock()
checker.neutron_check_segmentation_ids = MagicMock()
checker.neutron_check_l3_addresses_not_match_subnet_and_broadcast = \
MagicMock()
checker.check_public_floating_ranges_intersection = MagicMock()
checker.check_network_address_spaces_intersection = MagicMock()
checker.check_networks_amount = MagicMock()
checker.check_vlan_ids_range_and_intersection = MagicMock()
checker.check_network_classes_exclude_loopback = MagicMock()
checker.check_network_addresses_not_match_subnet_and_broadcast = \
MagicMock()
checker.check_configuration()
not_called = [
'check_public_floating_ranges_intersection',
'check_network_address_spaces_intersection',
'check_networks_amount',
'check_vlan_ids_range_and_intersection'
]
for method in not_called:
mocked = getattr(checker, method)
self.assertFalse(mocked.called)
called = [
'neutron_check_network_address_spaces_intersection',
'neutron_check_segmentation_ids',
'neutron_check_l3_addresses_not_match_subnet_and_broadcast',
'check_network_classes_exclude_loopback',
'check_network_addresses_not_match_subnet_and_broadcast'
]
for method in called:
mocked = getattr(checker, method)
mocked.assert_any_call()
def test_check_configuration_nova_network(self):
checker = NetworkCheck(self.task, {})
checker.net_provider = 'nova-network'
checker.neutron_check_network_address_spaces_intersection = MagicMock()
checker.neutron_check_segmentation_ids = MagicMock()
checker.neutron_check_l3_addresses_not_match_subnet_and_broadcast = \
MagicMock()
checker.check_public_floating_ranges_intersection = MagicMock()
checker.check_network_address_spaces_intersection = MagicMock()
checker.check_networks_amount = MagicMock()
checker.check_vlan_ids_range_and_intersection = MagicMock()
checker.check_network_classes_exclude_loopback = MagicMock()
checker.check_network_addresses_not_match_subnet_and_broadcast = \
MagicMock()
checker.check_configuration()
not_called = [
'neutron_check_network_address_spaces_intersection',
'neutron_check_segmentation_ids',
'neutron_check_l3_addresses_not_match_subnet_and_broadcast'
]
for method in not_called:
mocked = getattr(checker, method)
self.assertFalse(mocked.called)
called = [
'check_public_floating_ranges_intersection',
'check_network_address_spaces_intersection',
'check_networks_amount',
'check_vlan_ids_range_and_intersection',
'check_network_classes_exclude_loopback',
'check_network_addresses_not_match_subnet_and_broadcast'
]
for method in called:
mocked = getattr(checker, method)
mocked.assert_any_call()
@patch.object(NetworkCheck, 'check_untagged_intersection')
@patch.object(NetworkCheck, 'check_bond_slaves_speeds')
def test_check_interface_mapping(self, mock_untagged, mock_bond):
checker = NetworkCheck(self.task, {})
checker.check_interface_mapping()
mock_untagged.assert_called_with()
mock_bond.assert_called_with()
|
# Copyright (C) 2021-2022 Intel Corporation
# SPDX-License-Identifier: Apache-2.0
"""MXNet Framework Adapter plugin."""
from pickle import dumps
from pickle import loads
from typing import Dict
import mxnet as mx
import numpy as np
from mxnet import nd
from openfl.plugins.frameworks_adapters.framework_adapter_interface import (
FrameworkAdapterPluginInterface
)
class FrameworkAdapterPlugin(FrameworkAdapterPluginInterface):
"""Framework adapter plugin class."""
def __init__(self) -> None:
"""Initialize framework adapter."""
@staticmethod
def get_tensor_dict(model, optimizer=None) -> Dict[str, np.ndarray]:
"""
Extract tensor dict from a model and an optimizer.
Returns:
dict {weight name: numpy ndarray}
"""
state = {}
if optimizer is not None:
state = _get_optimizer_state(optimizer)
model_params = model.collect_params()
for param_name, param_tensor in model_params.items():
if isinstance(param_tensor.data(), mx.ndarray.ndarray.NDArray):
state[param_name] = param_tensor.list_data()[0].asnumpy()
return state
@staticmethod
def set_tensor_dict(model, tensor_dict: Dict[str, np.ndarray],
optimizer=None, device=None) -> None:
"""
Set tensor dict from a model and an optimizer.
Given a dict {weight name: numpy ndarray} sets weights to
the model and optimizer objects inplace.
"""
if device is not None:
device = mx.cpu() if device.startswith('cpu') else (
mx.gpu(int(device.split(':')[1].strip()))
)
if optimizer is not None:
_set_optimizer_state(optimizer, device, tensor_dict)
model.collect_params().reset_ctx(device)
model_params = model.collect_params()
for param_name in model_params:
model_params[param_name].set_data(nd.array(tensor_dict.pop(param_name), ctx=device))
def _get_optimizer_state(optimizer):
"""Return the optimizer state.
Args:
optimizer
"""
states = loads(optimizer._updaters[0].get_states(dump_optimizer=False))
result_states = {}
for state_key, state_tuple in states.items():
for state_ind, state in enumerate(state_tuple):
result_states[f'opt_state__{state_key}__{state_ind}'] = state.asnumpy()
return result_states
def _set_optimizer_state(optimizer, device, opt_state_dict):
"""Set the optimizer state.
Args:
optimizer:
device:
"""
state_keys, max_numstates = set(), 0
for key in opt_state_dict.keys():
if not key.startswith('opt_state'):
continue
_, part1, part2 = key.split('__')
state_keys.add(int(part1))
max_numstates = max(max_numstates, int(part2))
out_state = {}
for _ in range(len(state_keys)):
key = state_keys.pop()
state_vals = []
for i in range(max_numstates + 1):
state_vals.append(nd.array(opt_state_dict.pop(f'opt_state__{key}__{i}'), ctx=device))
out_state[key] = tuple(state_vals)
optimizer._updaters[0].set_states(dumps(out_state))
|
import datetime as dt
from django.dispatch import receiver
from django.urls import reverse
from django.utils.timezone import now
from django.utils.translation import gettext_lazy as _
from django_scopes import scope
from pretalx.common.models.settings import hierarkey
from pretalx.common.signals import periodic_task
from pretalx.event.models import Event
from pretalx.orga.signals import nav_event_settings
from .tasks import task_refresh_upstream_schedule
hierarkey.add_default("downstream_interval", 15)
hierarkey.add_default("downstream_checking_time", "event")
@receiver(periodic_task)
def refresh_upstream_schedule(sender, request=None, **kwargs):
_now = now()
for event in Event.objects.all():
with scope(event=event):
if not event.settings.downstream_upstream_url:
continue
if not _now < (event.datetime_to + dt.timedelta(days=1)):
continue
if not (
event.settings.downstream_checking_time == "always"
or event.datetime_from < _now
):
continue
try:
interval = int(event.settings.downstream_interval)
except TypeError:
interval = 5
interval = dt.timedelta(minutes=interval)
last_pulled = event.settings.upstream_last_sync
if (
not last_pulled
or _now - dt.datetime.strptime(last_pulled, "%Y-%m-%dT%H:%M:%S.%f%z")
> interval
):
task_refresh_upstream_schedule.apply_async(
kwargs={"event_slug": event.slug}
)
if event.upstream_results.count() > 3:
latest_three = list(event.upstream_results.order_by("-timestamp")[:3])
event.upstream_results.filter(
timestamp__lt=latest_three[-1].timestamp
).delete()
@receiver(nav_event_settings)
def register_upstream_settings(sender, request, **kwargs):
if not request.user.has_perm("orga.change_settings", request.event):
return []
return [
{
"label": _("Upstream"),
"url": reverse(
"plugins:pretalx_downstream:settings",
kwargs={"event": request.event.slug},
),
"active": request.resolver_match.url_name
== "plugins:pretalx_downstream:settings",
}
]
|
"""
This file contains functions to convert CML style puncturing configurations
for turbo codes to "interleaving sequences" good for the IT++ implementation
"""
import numpy as np
def getInterleaving(msg_len, num_g1, num_g2, constraint_length, punc1, punc2,
tail1, tail2):
"""
Returns, a list where there is an element for each bit in the punctured
output seqeuence, where in the IT++ sequence it was taken from
@param msg_len: the length of the message being encoded
@param num_g1: the number of generators in the first encoder
@param num_g2: the number of generators in the second encoder
@param constraint_length: the constraint length of the code. There will be
constraint_length - 1 bits in the tail of each encoder
@param punc1: a matrix specifying the puncturing schedule of non-tail bits
of the first encoder
@param punc2: a matrix specifying the puncturing schedule of non-tail bits
of the second encoder
@param tail1: a matrix specifying the puncturing schedule of tail bits
of the first encoder
@param tail2: a matrix specifying the puncturing schedule of tail bits
of the second encoder
"""
sequence = []
assert(punc1.shape[0] == num_g1)
assert(punc2.shape[0] == num_g2)
assert(tail1.shape == (num_g1, num_g1))
assert(tail2.shape == (num_g2, num_g2))
N = num_g1 + num_g2 - 1
# the IT++ encoder punctures the systematic bits from second encoder
assert (punc2[0,:] == 0).all()
heartPunc = np.concatenate((punc1, punc2[1:,:]), axis = 0)
# take column after column, to produce the sequence
heartPunc = np.reshape(heartPunc, -1, order='F')
# reshape the tail vectors
tailPunc1 = tail1.reshape(-1, order='F')
tailPunc2 = tail2.reshape(-1, order='F')
# number of tail bits
kk = constraint_length - 1
# get heart's interleaving sequence
for i in xrange(N * msg_len):
sequence.extend([i] * heartPunc[i % heartPunc.size])
# get tail's interleaving sequence. this should take care of the different
# ordering of tail bits between CML and IT++, where CML puts takes a tail
# bit from every generator in both encoders and then the next tail bit, and
# CML first takes every bit from first encoder then every bit from second.
for i in xrange(kk):
# take the few bits from first tail
for j in xrange(num_g1):
sequence.extend([(N * msg_len) + (i * num_g1) + j] * tailPunc1[(i * num_g1 + j) % tailPunc1.size])
# take the few bits from second tail
for j in xrange(num_g2):
sequence.extend([(N * msg_len) + (kk * num_g1) + (i * num_g2) + j] * tailPunc2[(i * num_g2 + j) % tailPunc2.size])
return sequence
def getCDMA2000(scenario):
"""
Gets the output puncturing/interleaving sequence for CDMA2000's scenario as
declared in CML's Cdma2000Scenarios.m
"""
if scenario in [1,2,3,4]:
return getInterleaving(msg_len=12282, num_g1=3, num_g2=3,
constraint_length=4,
punc1 = np.array(np.mat('1 1; 1 1; 1 0')),
punc2 = np.array(np.mat('0 0; 0 1; 1 1')),
tail1 = np.array(np.mat('2 2 2; 1 1 1; 1 1 1')),
tail2 = np.array(np.mat('2 2 2; 1 1 1; 1 1 1')))
elif scenario == 5:
return getInterleaving(msg_len=1530, num_g1=3, num_g2=3,
constraint_length=4,
punc1 = np.array(np.mat('1 1; 1 1; 1 1')),
punc2 = np.array(np.mat('0 0; 1 1; 1 1')),
tail1 = np.array(np.mat('3 3 3; 1 1 1; 1 1 1')),
tail2 = np.array(np.mat('3 3 3; 1 1 1; 1 1 1')))
elif scenario == 6:
return getInterleaving(msg_len=1530, num_g1=3, num_g2=3,
constraint_length=4,
punc1 = np.array(np.mat('1 1; 1 1; 1 0')),
punc2 = np.array(np.mat('0 0; 0 1; 1 1')),
tail1 = np.array(np.mat('2 2 2; 1 1 1; 1 1 1')),
tail2 = np.array(np.mat('2 2 2; 1 1 1; 1 1 1')))
elif scenario == 7:
return getInterleaving(msg_len=1530, num_g1=2, num_g2=2,
constraint_length=4,
punc1 = np.array(np.mat('1 1; 1 1')),
punc2 = np.array(np.mat('0 0; 1 1')),
tail1 = np.array(np.mat('2 2 2; 1 1 1')),
tail2 = np.array(np.mat('2 2 2; 1 1 1')))
elif scenario == 8:
return getInterleaving(msg_len=1530, num_g1=2, num_g2=2,
constraint_length=4,
punc1 = np.array(np.mat('1 1; 1 0')),
punc2 = np.array(np.mat('0 0; 0 1')),
tail1 = np.array(np.mat('1 1 1; 1 1 1')),
tail2 = np.array(np.mat('1 1 1; 1 1 1')))
|
__author__ = 'bartek'
from py2neo import Node, Relationship
class Groups:
LABEL = "GROUP"
@staticmethod
def create_group(db, name, owner):
node = Node(Groups.LABEL, name=name)
db.create(node)
rel = Relationship(owner, Relationships.OWNS, node)
db.create(rel)
@staticmethod
def add_user(db, group, user):
rel = Relationship(user, Relationships.IS_MEMBER, group)
db.create(rel)
class Relationships:
IS_MEMBER = "IS_MEMBER"
OWNS = "OWNS" |
import re
import argparse
def fastq_to_fasta(fastq_in, fasta_out=None):
# idea copied from Humann2
with open(fastq_in, "r") as fp_fastq_in:
fp_fasta_out = None
if fasta_out:
fp_fasta_out = open(fasta_out, "w")
line = fp_fastq_in.readline()
while line:
if re.search(r'^@', line):
sequence_id = line.replace("@", ">", 1).rstrip()
line = fp_fastq_in.readline()
sequence=""
while line:
if re.search(r'^\+', line):
if not fp_fasta_out:
print(sequence_id)
print(sequence)
else:
fp_fasta_out.write(sequence_id+"\n")
fp_fasta_out.write(sequence+"\n")
break
else:
sequence += line.rstrip()
line = fp_fastq_in.readline()
line = fp_fastq_in.readline()
if fp_fasta_out:
fp_fasta_out.close()
return
def main():
parser = argparse.ArgumentParser()
parser.add_argument("fastq", help="input fastq")
parser.add_argument("--fasta", default=None, help=("output fasta. If not"
" specified, the output will be printed to stdout"))
args = parser.parse_args()
fastq_to_fasta(args.fastq, args.fasta)
if __name__ == "__main__":
main()
|
from sqlalchemy import Column, Integer, String
from .views import db
class MemberOfParliament(db.Model):
def __init__(self, url=None, profile_pic=None, name=None, detail=None, party=None, gender=None):
self.url = url
self.profile_pic = profile_pic
self.name = name
self.detail = detail
self.party = party
self.gender = gender
if url:
self.key = url.split('/')[-2]
return
__tablename__ = 'members'
# columns
pk = Column(Integer, primary_key=True)
name = Column(String)
gender = Column(String)
url = Column(String)
party = Column(String)
profile_pic = Column(String)
key = Column(String)
score = Column(Integer, default=0)
def __repr__(self):
return "<MemberOfParliament(pk='%s', name='%s')>" % (
str(self.pk), str(self.name))
def as_dict(self):
tmp = {c.name: getattr(self, c.name) for c in self.__table__.columns}
del tmp['pk']
del tmp['key']
tmp['id'] = self.key
return tmp
|
# Dumping Format
# [
# {
# "contact": 0/1,
# "region": target_region,
# "anchor_id": anchor_list,
# "anchor_elasti": elasti_mat.tolist(),
# }
# ]
# and
# {
# "object_tsl": np.array(3,)
# "object_rot": np.array(3,3)
# "hand_tsl": np.array(3,)
# "hand_rot": np.array(3,3)
# "hand_shape": np.array(10,)
# }
import os
import pickle
from abc import ABC, abstractmethod
import torch
from manopth.anchorutils import anchor_load, get_rev_anchor_mapping
from hocontact.hodatasets.hoquery import BaseQueries, MetaQueries, CollateQueries
class Dumper(ABC):
def __init__(self, dump_prefix, anchor_root):
self.dump_prefix = dump_prefix
_, _, _, self.anchor_mapping = anchor_load(anchor_root)
self.rev_anchor_mapping = get_rev_anchor_mapping(self.anchor_mapping)
self.counter = 0
@abstractmethod
def info(self):
pass
@abstractmethod
def feed_and_dump(self, sample, results):
pass
class PicrOfflineDumper(Dumper):
def __init__(self, dump_prefix, anchor_root):
super().__init__(dump_prefix, anchor_root)
self.type = "PicrOfflineDumper"
def info(self):
res = f"{self.type}\n"
res += f" prefix: {self.dump_prefix}\n"
res += f" count: {self.counter}"
return res
def feed_and_dump(self, sample, results, vc_thresh):
# get sample identifier
sample_identifier = sample[MetaQueries.SAMPLE_IDENTIFIER]
n_sample = len(sample_identifier)
collate_mask = sample[CollateQueries.PADDING_MASK] # TENSOR[B, N]
# assert fields in results
assert "recov_vertex_contact" in results, f"{self.type}: vertex_contact not found"
assert "recov_contact_region" in results, f"{self.type}: contact_region not found"
assert "recov_anchor_elasti" in results, f"{self.type}: anchor_elasti not found"
recov_vertex_contact = results["recov_vertex_contact"].detach() # TENSOR[B, N]
recov_contact_in_image_mask = results["recov_contact_in_image_mask"].detach() # TENSOR[B, N]
recov_contact_region = results["recov_contact_region"].detach() # TENSOR[B, N, 17]
recov_anchor_elasti_pred = results["recov_anchor_elasti"].detach() # TENSOR[B, N, 4]
recov_vertex_contact_pred = (torch.sigmoid(recov_vertex_contact) > vc_thresh).bool() # TENSOR[B, N]
recov_contact_region_pred = torch.argmax(recov_contact_region, dim=2) # TENSOR[B, N]
# iterate over samples, assemble dump dict
for idx in range(n_sample):
sample_id = sample_identifier[idx]
sample_collate_mask = collate_mask[idx, :].bool() # TENSOR[N, ]
sample_vertex_contact = recov_vertex_contact_pred[idx, :] # TENSOR[N, ]
sample_contact_in_image_mask = recov_contact_in_image_mask[idx, :] # TENSOR[N, ]
combined_vertex_contact = sample_vertex_contact.bool() & sample_contact_in_image_mask.bool() # TENSOR[N,]
filtered_vertex_contact = combined_vertex_contact[sample_collate_mask] # TENSOR[X, ]
sample_contact_region = recov_contact_region_pred[idx, :] # TENSOR[N, ]
filtered_contact_region = sample_contact_region[sample_collate_mask] # TENSOR[X, ]
sample_anchor_elasti = recov_anchor_elasti_pred[idx, :, :] # TENSOR[N, 4]
filtered_anchor_elasti = sample_anchor_elasti[sample_collate_mask, :] # TENSOR[X, 4]
# transport from cuda to cpu
filtered_vertex_contact = filtered_vertex_contact.cpu()
filtered_contact_region = filtered_contact_region.cpu()
filtered_anchor_elasti = filtered_anchor_elasti.cpu()
# iterate over all points
sample_res = []
n_points = filtered_vertex_contact.shape[0] # X
for p_idx in range(n_points):
p_contact = int(filtered_vertex_contact[p_idx])
if p_contact == 0:
p_res = {
"contact": 0,
}
else: # p_contact == 1
p_region = int(filtered_contact_region[p_idx])
p_anchor_id = self.rev_anchor_mapping[p_region]
p_n_anchor = len(p_anchor_id)
p_anchor_elasti = filtered_anchor_elasti[p_idx, :p_n_anchor].tolist()
p_res = {
"contact": 1,
"region": p_region,
"anchor_id": p_anchor_id,
"anchor_elasti": p_anchor_elasti,
}
sample_res.append(p_res)
# save sample_res
save_path = os.path.join(self.dump_prefix, f"{sample_id}.pkl")
save_dir = os.path.dirname(save_path)
os.makedirs(save_dir, exist_ok=True)
with open(save_path, "wb") as fstream:
pickle.dump(sample_res, fstream)
self.counter += 1
class PicrDumper(Dumper):
def __init__(self, dump_prefix, anchor_root):
super().__init__(dump_prefix, anchor_root)
self.type = "PicrDumper"
self.honet_fields = [
"hand_tsl",
"hand_joints_3d",
"hand_verts_3d",
"hand_full_pose",
"hand_shape",
"obj_tsl",
"obj_rot",
"obj_verts_3d",
]
def info(self):
res = f"{self.type}\n"
res += f" prefix: {self.dump_prefix}\n"
res += f" count: {self.counter}"
return res
def feed_and_dump(self, sample, results, vc_thresh):
# get sample identifier
sample_identifier = sample[MetaQueries.SAMPLE_IDENTIFIER]
n_sample = len(sample_identifier)
collate_mask = sample[CollateQueries.PADDING_MASK] # TENSOR[B, N]
# ====== assert fields in results: contact related
assert "recov_vertex_contact" in results, f"{self.type}: vertex_contact not found"
assert "recov_contact_region" in results, f"{self.type}: contact_region not found"
assert "recov_anchor_elasti" in results, f"{self.type}: anchor_elasti not found"
recov_vertex_contact = results["recov_vertex_contact"].detach() # TENSOR[B, N]
recov_contact_in_image_mask = results["recov_contact_in_image_mask"].detach() # TENSOR[B, N]
recov_contact_region = results["recov_contact_region"].detach() # TENSOR[B, N, 17]
recov_anchor_elasti_pred = results["recov_anchor_elasti"].detach() # TENSOR[B, N, 4]
recov_vertex_contact_pred = (torch.sigmoid(recov_vertex_contact) > vc_thresh).bool() # TENSOR[B, N]
recov_contact_region_pred = torch.argmax(recov_contact_region, dim=2) # TENSOR[B, N]
# ====== assert fields in results: honet related
for field in self.honet_fields:
assert field in results, f"{self.type}: {field} not found"
# iterate over samples, assemble dump dict
for idx in range(n_sample):
sample_id = sample_identifier[idx]
# ==================== dump contact related info >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
sample_collate_mask = collate_mask[idx, :].bool() # TENSOR[N, ]
sample_vertex_contact = recov_vertex_contact_pred[idx, :] # TENSOR[N, ]
sample_contact_in_image_mask = recov_contact_in_image_mask[idx, :] # TENSOR[N, ]
combined_vertex_contact = sample_vertex_contact.bool() & sample_contact_in_image_mask.bool() # TENSOR[N,]
filtered_vertex_contact = combined_vertex_contact[sample_collate_mask] # TENSOR[X, ]
sample_contact_region = recov_contact_region_pred[idx, :] # TENSOR[N, ]
filtered_contact_region = sample_contact_region[sample_collate_mask] # TENSOR[X, ]
sample_anchor_elasti = recov_anchor_elasti_pred[idx, :, :] # TENSOR[N, 4]
filtered_anchor_elasti = sample_anchor_elasti[sample_collate_mask, :] # TENSOR[X, 4]
# transport from cuda to cpu
filtered_vertex_contact = filtered_vertex_contact.cpu()
filtered_contact_region = filtered_contact_region.cpu()
filtered_anchor_elasti = filtered_anchor_elasti.cpu()
# iterate over all points
sample_res = []
n_points = filtered_vertex_contact.shape[0] # X
for p_idx in range(n_points):
p_contact = int(filtered_vertex_contact[p_idx])
if p_contact == 0:
p_res = {
"contact": 0,
}
else: # p_contact == 1
p_region = int(filtered_contact_region[p_idx])
p_anchor_id = self.rev_anchor_mapping[p_region]
p_n_anchor = len(p_anchor_id)
p_anchor_elasti = filtered_anchor_elasti[p_idx, :p_n_anchor].tolist()
p_res = {
"contact": 1,
"region": p_region,
"anchor_id": p_anchor_id,
"anchor_elasti": p_anchor_elasti,
}
sample_res.append(p_res)
# save sample_res
save_path = os.path.join(self.dump_prefix, f"{sample_id}_contact.pkl")
save_dir = os.path.dirname(save_path)
os.makedirs(save_dir, exist_ok=True)
with open(save_path, "wb") as fstream:
pickle.dump(sample_res, fstream)
# <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
# ==================== dump honet related info >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
honet_res = {}
for field in self.honet_fields:
if field in ["obj_verts_3d"]:
honet_res[field] = results[field][idx, ...][sample_collate_mask, :].detach().cpu().numpy()
honet_res[field] = results[field][idx, ...].detach().cpu().numpy()
honet_res["image_path"] = sample[BaseQueries.IMAGE_PATH][idx]
honet_save_path = os.path.join(self.dump_prefix, f"{sample_id}_honet.pkl")
with open(honet_save_path, "wb") as fstream:
pickle.dump(honet_res, fstream)
# <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
self.counter += 1
|
from presurvey.models import BostonZip
b = BostonZip(zipcode='01760', name='Framingham')
b.save()
b = BostonZip(zipcode='01730', name='Bedford')
b.save()
b = BostonZip(zipcode='01731', name='Hanscom Air Force Base')
b.save()
b = BostonZip(zipcode='01773', name='Lincoln')
b.save()
b = BostonZip(zipcode='01801', name='Woburn')
b.save()
b = BostonZip(zipcode='01803', name='Burlington')
b.save()
b = BostonZip(zipcode='01867', name='Reading')
b.save()
b = BostonZip(zipcode='01880', name='Wakefield')
b.save()
b = BostonZip(zipcode='01887', name='Wilmington')
b.save()
b = BostonZip(zipcode='01890', name='Winchester')
b.save()
b = BostonZip(zipcode='01902', name='Lynn')
b.save()
b = BostonZip(zipcode='01904', name='East Lynn')
b.save()
b = BostonZip(zipcode='01905', name='West Lynn')
b.save()
b = BostonZip(zipcode='01906', name='Saugus')
b.save()
b = BostonZip(zipcode='01907', name='Swampscott')
b.save()
b = BostonZip(zipcode='01908', name='Nahant')
b.save()
b = BostonZip(zipcode='01940', name='Lynnfield')
b.save()
b = BostonZip(zipcode='01945', name='Marblehead')
b.save()
b = BostonZip(zipcode='01960', name='Peabody')
b.save()
b = BostonZip(zipcode='01970', name='Salem')
b.save()
b = BostonZip(zipcode='02021', name='Canton')
b.save()
b = BostonZip(zipcode='02025', name='Cohasset')
b.save()
b = BostonZip(zipcode='02026', name='Dedham')
b.save()
b = BostonZip(zipcode='02030', name='Dover')
b.save()
b = BostonZip(zipcode='02043', name='Hingham')
b.save()
b = BostonZip(zipcode='02045', name='Hull')
b.save()
b = BostonZip(zipcode='02062', name='Norwood')
b.save()
b = BostonZip(zipcode='02090', name='Westwood')
b.save()
b = BostonZip(zipcode='02108', name='Boston')
b.save()
b = BostonZip(zipcode='02109', name='Boston')
b.save()
b = BostonZip(zipcode='02110', name='Boston')
b.save()
b = BostonZip(zipcode='02111', name='Boston')
b.save()
b = BostonZip(zipcode='02113', name='Boston')
b.save()
b = BostonZip(zipcode='02114', name='Boston')
b.save()
b = BostonZip(zipcode='02115', name='Boston')
b.save()
b = BostonZip(zipcode='02116', name='Boston')
b.save()
b = BostonZip(zipcode='02118', name='Roxbury')
b.save()
b = BostonZip(zipcode='02119', name='Roxbury')
b.save()
b = BostonZip(zipcode='02120', name='Roxbury')
b.save()
b = BostonZip(zipcode='02121', name='Dorchester')
b.save()
b = BostonZip(zipcode='02122', name='Dorchester')
b.save()
b = BostonZip(zipcode='02124', name='Dorchester')
b.save()
b = BostonZip(zipcode='02125', name='Dorchester')
b.save()
b = BostonZip(zipcode='02126', name='Mattapan')
b.save()
b = BostonZip(zipcode='02127', name='South Boston')
b.save()
b = BostonZip(zipcode='02128', name='East Boston')
b.save()
b = BostonZip(zipcode='02129', name='Charlestown')
b.save()
b = BostonZip(zipcode='02130', name='Jamaica Plain')
b.save()
b = BostonZip(zipcode='02131', name='Roslindale')
b.save()
b = BostonZip(zipcode='02132', name='West Roxbury')
b.save()
b = BostonZip(zipcode='02134', name='Allston')
b.save()
b = BostonZip(zipcode='02135', name='Brighton')
b.save()
b = BostonZip(zipcode='02136', name='Hyde Park')
b.save()
b = BostonZip(zipcode='02138', name='Cambridge')
b.save()
b = BostonZip(zipcode='02139', name='Cambridge')
b.save()
b = BostonZip(zipcode='02140', name='North Cambridge')
b.save()
b = BostonZip(zipcode='02141', name='East Cambridge')
b.save()
b = BostonZip(zipcode='02142', name='Cambridge')
b.save()
b = BostonZip(zipcode='02143', name='Somerville')
b.save()
b = BostonZip(zipcode='02144', name='Somerville')
b.save()
b = BostonZip(zipcode='02145', name='Somerville')
b.save()
b = BostonZip(zipcode='02148', name='Malden')
b.save()
b = BostonZip(zipcode='02149', name='Everett')
b.save()
b = BostonZip(zipcode='02150', name='Chelsea')
b.save()
b = BostonZip(zipcode='02151', name='Revere')
b.save()
b = BostonZip(zipcode='02152', name='Winthrop')
b.save()
b = BostonZip(zipcode='02155', name='Medford')
b.save()
b = BostonZip(zipcode='02163', name='Cambridge')
b.save()
b = BostonZip(zipcode='02169', name='Quincy')
b.save()
b = BostonZip(zipcode='02170', name='Quincy')
b.save()
b = BostonZip(zipcode='02171', name='Quincy')
b.save()
b = BostonZip(zipcode='02176', name='Melrose')
b.save()
b = BostonZip(zipcode='02180', name='Stoneham')
b.save()
b = BostonZip(zipcode='02184', name='Braintree')
b.save()
b = BostonZip(zipcode='02186', name='Milton')
b.save()
b = BostonZip(zipcode='02188', name='Weymouth')
b.save()
b = BostonZip(zipcode='02189', name='Weymouth')
b.save()
b = BostonZip(zipcode='02190', name='Weymouth')
b.save()
b = BostonZip(zipcode='02191', name='Weymouth')
b.save()
b = BostonZip(zipcode='02199', name='Boston')
b.save()
b = BostonZip(zipcode='02210', name='Boston')
b.save()
b = BostonZip(zipcode='02215', name='Boston')
b.save()
b = BostonZip(zipcode='02222', name='Boston')
b.save()
b = BostonZip(zipcode='02343', name='Holbrook')
b.save()
b = BostonZip(zipcode='02368', name='Randolph')
b.save()
b = BostonZip(zipcode='02420', name='Lexington')
b.save()
b = BostonZip(zipcode='02421', name='Lexington')
b.save()
b = BostonZip(zipcode='02445', name='Brookline')
b.save()
b = BostonZip(zipcode='02446', name='Brookline')
b.save()
b = BostonZip(zipcode='02451', name='Waltham')
b.save()
b = BostonZip(zipcode='02452', name='Waltham')
b.save()
b = BostonZip(zipcode='02453', name='Waltham')
b.save()
b = BostonZip(zipcode='02458', name='Newton')
b.save()
b = BostonZip(zipcode='02459', name='Newton Center')
b.save()
b = BostonZip(zipcode='02460', name='Newtonville')
b.save()
b = BostonZip(zipcode='02461', name='Newton Highlands')
b.save()
b = BostonZip(zipcode='02462', name='Newton Lower')
b.save()
b = BostonZip(zipcode='02464', name='Newton Upper')
b.save()
b = BostonZip(zipcode='02465', name='West Newton')
b.save()
b = BostonZip(zipcode='02466', name='Auburndale')
b.save()
b = BostonZip(zipcode='02467', name='Chestnut Hill')
b.save()
b = BostonZip(zipcode='02468', name='Waban')
b.save()
b = BostonZip(zipcode='02472', name='Watertown')
b.save()
b = BostonZip(zipcode='02474', name='Arlington')
b.save()
b = BostonZip(zipcode='02476', name='Arlington')
b.save()
b = BostonZip(zipcode='02478', name='Belmont')
b.save()
b = BostonZip(zipcode='02481', name='Wellesley Hills')
b.save()
b = BostonZip(zipcode='02482', name='Wellesley')
b.save()
b = BostonZip(zipcode='02492', name='Needham')
b.save()
b = BostonZip(zipcode='02493', name='Weston')
b.save()
b = BostonZip(zipcode='02494', name='Needham Heights')
b.save()
|
# greaseweazle/tools/reset.py
#
# Greaseweazle control script: Reset to power-on defaults.
#
# Written & released by Keir Fraser <keir.xen@gmail.com>
#
# This is free and unencumbered software released into the public domain.
# See the file COPYING for more details, or visit <http://unlicense.org>.
description = "Reset the Greaseweazle device to power-on default state."
import sys
from greaseweazle.tools import util
from greaseweazle import usb as USB
def main(argv):
parser = util.ArgumentParser(usage='%(prog)s [options]')
parser.add_argument("--device", help="greaseweazle device name")
parser.description = description
parser.prog += ' ' + argv[1]
args = parser.parse_args(argv[2:])
try:
usb = util.usb_open(args.device)
usb.power_on_reset()
except USB.CmdError as error:
print("Command Failed: %s" % error)
if __name__ == "__main__":
main(sys.argv)
# Local variables:
# python-indent: 4
# End:
|
#!/usr/bin/env python3
""" 引数1=現在のAP,引数2までの時間,引数2がなければ40の倍数"""
import sys
import time
import datetime
APOverflow = "現在，APの最大値は139です。"
AP_LIMIT = 139
def error():
sys.exit(2)
""" ここまで回復"""
count = 0
if len(sys.argv) > 3:
error()
elif len(sys.argv) == 3:
if int(sys.argv[1]) >= int(sys.argv[2]):
error()
count = int(sys.argv[2])
elif len(sys.argv) == 2:
count = (int(sys.argv[1]) // 40 + 1) * 40
else:
error()
if int(count) >= AP_LIMIT:
error()
# 残り時間
leftMinute = (count - int(sys.argv[1])) * 5
hour = int(leftMinute / 60)
minute = leftMinute % 60
# 回復時刻
scheduledTimeUnix = int(time.time()) + (leftMinute * 60)
scheduledTime = datetime.datetime.fromtimestamp(scheduledTimeUnix).strftime("%H時%M分")
print("AP%sまで約%s時間%s分" % (count, hour, minute))
print(str(scheduledTime) + "までに回復予定")
|
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