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

1,1

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.

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A190534 A248466 A233407 * A167654 A095266 A232338

Adjacent sequences: A272136 A272137 A272138 * A272140 A272141 A272142

Keyword

nonn

Author

Paolo P. Lava, Apr 21 2016

Extensions

More terms from Altug Alkan, Apr 22 2016

Status

approved