A295770 Numbers k such that Bernoulli number B_{k} has denominator 4686.

70, 350, 4970, 5110, 7070, 8890, 9590, 9730, 13790, 15610, 15890, 16030, 17990, 18410, 19810, 21770, 22190, 23170, 24290, 25550, 26530, 26810, 27230, 28070, 30310, 32270, 32690, 33530, 34930, 36470, 38990, 39830, 40390, 43190, 44450, 45010, 48650, 49070, 49630, 51730

Offset

1,1

Comments

4686 = 2*3*11*71.

All terms are multiples of a(1) = 70.

For these numbers numerator(B_{k}) mod denominator(B_{k}) = 289.

Links

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

Example

Bernoulli B_{70} is 1505381347333367003803076567377857208511438160235/4686, hence 70 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, 4686);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 11, 71}:
select(filter, [seq(i, i=1..10^5)]);

Mathematica

70 Position[Array[Denominator@ BernoulliB[70 #] &, 10^3], 4686][[All, 1]] (* Michael De Vlieger, Nov 27 2017 *)
Select[70*Range[750], Denominator[BernoulliB[#]]==4686&] (* Harvey P. Dale, Nov 23 2023 *)

Prog

(PARI) isok(n) = denominator(bernfrac(n)) == 4686; \\ Michel Marcus, Nov 27 2017
(PARI) lista(nn) = forstep(n=70, nn, 70, if(denominator(bernfrac(n)) == 4686, print1(n, ", "))) \\ Iain Fox, Nov 27 2017

Crossrefs

Cf. A045979, A051222, A051225, A051226, A051227, A051228, A051229, A051230, A119456, A119480, A249134, A255684, A271634, A271635, A272138, A272139, A272140, A272183, A272184, A272185, A272186, A272369.

Sequence in context: A335861 A174533 A174534 * A151556 A172222 A157369

Adjacent sequences: A295767 A295768 A295769 * A295771 A295772 A295773

Keyword

nonn,easy

Author

Paolo P. Lava, Nov 27 2017

Status

approved