A092221 -id:A092221 - cp's OEIS frontend

A093058 Numbers k such that numerator of Bernoulli(2k) is divisible by the square of 59, the second irregular prime.

457, 1298, 2168, 3009, 3481, 3879, 4720, 5590, 6431, 6962, 7301, 8142, 9012, 9853, 10443, 10723, 11564, 12434, 13275, 13924, 14145, 14986, 15856, 16697, 17405, 17567, 18408

Offset: 1

Robert G. Wilson v, Feb 26 2004

nonn

Eric Weisstein's World of Mathematics, Bernoulli Number.

Cf. A000928, A091216, A092221.

Select[ Range[ 9695], Mod[ Numerator[ BernoulliB[2# ]], 59^2] == 0 &]

If we omit multiples of 3481 and take first differences, it appears that we get a common difference of {841, 870} repeated.

More terms from Eric W. Weisstein, Mar 19 2004

A093059 Numbers k such that the numerator of Bernoulli(2k) is divisible by the square of 67, the third irregular prime.

Original entry on oeis.org

1646, 1943, 3857, 4154, 4489, 6068, 6365, 8279, 8576, 8978, 10490, 10787, 12701, 12998, 13467, 14912, 15209, 17123, 17420, 17956

Offset: 1

Robert G. Wilson v, Feb 26 2004

nonn

Eric Weisstein's World of Mathematics, Bernoulli Number.

Cf. A000928, A091216, A092221.

Select[ Range[ 9695], Mod[ Numerator[ BernoulliB[2# ]], 67^2] == 0 &]

More terms from Eric W. Weisstein, Mar 19 2004

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

Original entry on oeis.org

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

Seiichi Manyama, Jan 23 2017

nonn

6 + 345*k and 100 + 345*k are terms for k >= 0.

			Bernoulli(2*6) = -691/2730. So 6 is a term.

Bernd C. Kellner, The Bernoulli Number Page.
Eric Weisstein's World of Mathematics, Bernoulli Number
Wikipedia, Kummer's congruences

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

Select[Range[4930],Mod[Numerator[BernoulliB[2#]],  691] == 0 &] (* Indranil Ghosh, Mar 11 2017 *)

is(n) = Mod(numerator(bernfrac(2*n)), 691)==0 \\ Felix Fröhlich, Jan 23 2017

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

a(n) = A119864(n)/2.

a(12) - a(36) from Seiichi Manyama, Jan 24 2017

More terms from Indranil Ghosh, Mar 11 2017

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A093058 Numbers k such that numerator of Bernoulli(2k) is divisible by the square of 59, the second irregular prime.

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A093059 Numbers k such that the numerator of Bernoulli(2k) is divisible by the square of 67, the third irregular prime.

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

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