A281502 Numbers m such that the numerator of Bernoulli(2m) is divisible by 691.

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

Table of n, a(n) for n=1..43.

Bernd C. Kellner, The Bernoulli Number Page.

Eric Weisstein's World of Mathematics, Bernoulli Number

Wikipedia, Kummer's congruences

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

Cf. A000928, A091216, A092221 - A092229, A119864.

Sequence in context: A192667 A360339 A127636 * A226413 A226344 A278430

Adjacent sequences: A281499 A281500 A281501 * A281503 A281504 A281505

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