A218755 -id:A218755 - cp's OEIS frontend

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

Paul Curtz, Nov 22 2012

nonn

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

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

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

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 *)

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

cp's OEIS Frontend

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

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