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%I #21 Jan 11 2016 03:11:44
%S 30,66,138,282,354,498,642,1002,1074,1362,1434,1578,2082,2154,2298,
%T 2478,2658,2730,2802,2874,3018,3378,3486,3522,3882,3954,4314,4494,
%U 4962,5034,5178,5322,5898,6114,7122,7338,7518,7554,7590,7698,7842,7914,8202,8634,8922
%N Denominators of Bernoulli numbers which are congruent to 3 (mod 9).
%C The sequence contains the elements of A090801 which are == 3 (mod 9).
%C Conjecture: all the first differences 36, 72, 144, 72,... of the sequence are multiples of 36.
%C The conjecture is true, since elements of A090801 are 2 mod 4. - _Charles R Greathouse IV_, Nov 22 2012
%H Charles R Greathouse IV, <a href="/A219543/b219543.txt">Table of n, a(n) for n = 1..10000</a>
%t 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 *)
%o (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
%Y Second subset of the Bernoulli denominators A090801. The first is A218755.
%K nonn
%O 1,1
%A _Paul Curtz_, Nov 22 2012
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