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A281502
Numbers m such that the numerator of Bernoulli(2m) is divisible by 691.
0
6, 100, 351, 445, 691, 696, 790, 1041, 1135, 1382, 1386, 1480, 1731, 1825, 2073, 2076, 2170, 2421, 2515, 2764, 2766, 2860, 3111, 3205, 3455, 3456, 3550, 3801, 3895, 4146, 4240, 4491, 4585, 4836, 4837, 4930, 5181, 5275, 5526, 5528, 5620, 5871, 5965
OFFSET
1,1
COMMENTS
6 + 345*k and 100 + 345*k are terms for k >= 0.
LINKS
Bernd C. Kellner, The Bernoulli Number Page.
Eric Weisstein's World of Mathematics, Bernoulli Number
FORMULA
a(n) = A119864(n)/2.
EXAMPLE
Bernoulli(2*6) = -691/2730. So 6 is a term.
MATHEMATICA
Select[Range[4930], Mod[Numerator[BernoulliB[2#]], 691] == 0 &] (* Indranil Ghosh, Mar 11 2017 *)
PROG
(PARI) is(n) = Mod(numerator(bernfrac(2*n)), 691)==0 \\ Felix Fröhlich, Jan 23 2017
(Python)
from itertools import count, islice
from sympy import bernoulli
def A281502gen(): return filter(lambda n:not bernoulli(2*n).p % 691, count(0))
A281502_list = list(islice(A281502gen(), 20)) # Chai Wah Wu, Dec 21 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 23 2017
EXTENSIONS
a(12) - a(36) from Seiichi Manyama, Jan 24 2017
More terms from Indranil Ghosh, Mar 11 2017
STATUS
approved