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%I #44 Dec 22 2021 10:18:08
%S 6,100,351,445,691,696,790,1041,1135,1382,1386,1480,1731,1825,2073,
%T 2076,2170,2421,2515,2764,2766,2860,3111,3205,3455,3456,3550,3801,
%U 3895,4146,4240,4491,4585,4836,4837,4930,5181,5275,5526,5528,5620,5871,5965
%N Numbers m such that the numerator of Bernoulli(2m) is divisible by 691.
%C 6 + 345*k and 100 + 345*k are terms for k >= 0.
%H Bernd C. Kellner, <a href="http://www.bernoulli.org/">The Bernoulli Number Page</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BernoulliNumber.html">Bernoulli Number</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kummer's_congruence">Kummer's congruences</a>
%F a(n) = A119864(n)/2.
%e Bernoulli(2*6) = -691/2730. So 6 is a term.
%t Select[Range[4930],Mod[Numerator[BernoulliB[2#]], 691] == 0 &] (* _Indranil Ghosh_, Mar 11 2017 *)
%o (PARI) is(n) = Mod(numerator(bernfrac(2*n)), 691)==0 \\ _Felix Fröhlich_, Jan 23 2017
%o (Python)
%o from itertools import count, islice
%o from sympy import bernoulli
%o def A281502gen(): return filter(lambda n:not bernoulli(2*n).p % 691,count(0))
%o A281502_list = list(islice(A281502gen(),20)) # _Chai Wah Wu_, Dec 21 2021
%Y Cf. A000928, A091216, A092221 - A092229, A119864.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Jan 23 2017
%E a(12) - a(36) from _Seiichi Manyama_, Jan 24 2017
%E More terms from _Indranil Ghosh_, Mar 11 2017
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