A295589 Numbers k such that Bernoulli number B_{k} has denominator 33330.

100, 1700, 7100, 16700, 22300, 25700, 28300, 31300, 31700, 33100, 35300, 37900, 38300, 38900, 39700, 44900, 45700, 47900, 52100, 56900, 58700, 60700, 66100, 75100, 75700, 78700, 79700, 83900, 85700, 85900, 88100, 90700, 96700, 99100

Offset

1,1

Comments

33330= 2*3*5*11*101.

All terms are multiples of a(1) = 100.

For these numbers numerator(B_{k}) mod denominator(B_{k}) = 28859.

Links

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

Example

Bernoulli B_{100} is
-945980378191221252952274330694937218727028415330669361333856962043113954151972 47711/33330, hence 100 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, 33330);
# Alternative: # according to Robert Israel code in A282773
with(numtheory): filter:= n ->
select(isprime, map(`+`, divisors(n), 1)) = {2, 3, 5, 11, 101}:
select(filter, [seq(i, i=1..10^5)]);

Mathematica

Select[Range[100, 100000, 100], Denominator[BernoulliB[#]]==33330&] (* Harvey P. Dale, Aug 05 2022 *)

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: A274943 A203283 A231139 * A114777 A128988 A075822

Adjacent sequences: A295586 A295587 A295588 * A295590 A295591 A295592

Keyword

nonn,easy

Author

Paolo P. Lava, Nov 24 2017

Status

approved