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
Keywords
Examples
Bernoulli(2*6) = -691/2730. So 6 is a term.
Links
- Bernd C. Kellner, The Bernoulli Number Page.
- Eric Weisstein's World of Mathematics, Bernoulli Number
- Wikipedia, Kummer's congruences
Programs
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Mathematica
Select[Range[4930],Mod[Numerator[BernoulliB[2#]], 691] == 0 &] (* Indranil Ghosh, Mar 11 2017 *)
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PARI
is(n) = Mod(numerator(bernfrac(2*n)), 691)==0 \\ Felix Fröhlich, Jan 23 2017
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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
Formula
a(n) = A119864(n)/2.
Extensions
a(12) - a(36) from Seiichi Manyama, Jan 24 2017
More terms from Indranil Ghosh, Mar 11 2017
Comments