A272139 Numbers n such that Bernoulli number B_{n} has denominator 1806.

42, 294, 798, 1806, 2058, 2814, 2982, 4074, 4578, 5334, 5586, 6594, 6846, 8106, 8274, 8358, 9366, 9534, 12642, 12894, 13314, 14154, 14658, 15162, 17178, 18186, 19194, 20118, 20454, 21882, 21966, 22722, 22974, 23982, 25914, 26502, 27006, 28266, 28518, 29778

Offset: 1

Author

Paolo P. Lava, Apr 21 2016

Keywords

• nonn

Comments

1806 = 2 * 3 * 7 * 43.

All terms are multiple of a(1) = 42.

For these numbers numerator(B_{n}) mod denominator(B_{n}) = 1.

In 2005, B. C. Kellner proved E. W. Weisstein's conjecture that denom(B_n) = n only if n = 1806.

Examples

			Bernoulli B_{42} is 1520097643918070802691/1806, hence 42 is in the sequence.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272140, A272183, A272184, A272185, A272186.

Programs

Maple

with(numtheory): P:=proc(q,h) local n;  for n from 2 by 2 to q do
if denom(bernoulli(n))=h then print(n); fi; od; end: P(10^6,1806);

Mathematica

Select[Range[0, 1000], Denominator[BernoulliB[#]] == 1806 &] (* Robert Price, Apr 21 2016 *)
Select[Range[42,30000,42],Denominator[BernoulliB[#]]==1806&] (* Harvey P. Dale, Jun 01 2019 *)

PARI

lista(nn) = for(n=1, nn, if(denominator(bernfrac(n)) == 1806, print1(n, ", "))); \\ Altug Alkan, Apr 22 2016

Extensions

More terms from Altug Alkan, Apr 22 2016