A219543 Denominators of Bernoulli numbers which are congruent to 3 (mod 9).

30, 66, 138, 282, 354, 498, 642, 1002, 1074, 1362, 1434, 1578, 2082, 2154, 2298, 2478, 2658, 2730, 2802, 2874, 3018, 3378, 3486, 3522, 3882, 3954, 4314, 4494, 4962, 5034, 5178, 5322, 5898, 6114, 7122, 7338, 7518, 7554, 7590, 7698, 7842, 7914, 8202, 8634, 8922

Offset

1,1

Comments

The sequence contains the elements of A090801 which are == 3 (mod 9).

Conjecture: all the first differences 36, 72, 144, 72,... 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

Mathematica

listLength = 50; n0 = 10*listLength; Clear[f]; f[n_] := f[n] = Union[Reap[ For[k = 4, k <= n, k = k+2, b = Denominator[BernoulliB[k]]; If[Mod[b, 36] == 30, Sow[b]]]][[2, 1]]][[1 ;; listLength]]; f[n0]; f[n = 2 n0]; While[ Print["n = ", n]; f[n] != f[n/2], n = 2 n]; A219543 = f[n] (* Jean-François Alcover, Jan 11 2016 *)

Prog

(PARI) is(n)=if(n%36-30, 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

Crossrefs

Second subset of the Bernoulli denominators A090801. The first is A218755.

Sequence in context: A209876 A290145 A157346 * A309393 A154055 A270758

Adjacent sequences: A219540 A219541 A219542 * A219544 A219545 A219546

Keyword

nonn

Author

Paul Curtz, Nov 22 2012

Status

approved