A218755 Denominators of Bernoulli numbers which are == 6 (mod 9).

6, 42, 330, 510, 690, 798, 870, 1410, 1518, 1590, 1770, 1806, 2490, 3102, 3210, 3318, 3894, 4110, 4326, 4470, 4686, 5010, 5190, 5370, 5478, 6486, 6810, 7062, 7890, 8070, 8142, 8646, 8790, 9366, 9510, 10410, 10770, 11022

Offset: 1

Author

Paul Curtz, Nov 05 2012

Keywords

• nonn
• easy

Comments

The sequence contains the elements of A090801 which are == 6 (mod 9).

Conjecture: all first differences 36, 288, 180, 180,... of the sequence are multiples of 36.

The conjecture is true, since elements of A090801 are 2 mod 4. - Charles R Greathouse IV, Nov 22 2012

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Second subset of the Bernoulli denominators: A090801 which are == 3 (mod 9).

Programs

Mathematica

Take[Union[Select[Denominator[BernoulliB[Range[1000]]],Mod[#,9]==6&]],60] (* Harvey P. Dale, Nov 28 2012 *)

PARI

is(n)=if(n%36-6, 0, my(f=factor(n)); if(vecmax(f[, 2])>1, return(0)); fordiv(lcm(apply(k->k-1, f[, 1])), k, if(isprime(k+1) && n%(k+1), return(0))); 1) \\ Charles R Greathouse IV, Nov 26 2012