cp's OEIS Frontend

A212615 Least k > 1 such that the product pen(n) * pen(k) is pentagonal, or zero if no such k exists, where pen(k) is the k-th pentagonal number.

%I A212615 #9 Mar 13 2015 00:15:20
%S A212615 2,39,2231,40,14,94974,47,212,1071,477,124,261,15120,5,180,375638,
%T A212615 2413,22,4270831,924,278,18,126,33510,355,376,9047610,37313170,
%U A212615 1533015,7315,1687018,520,363155,8827,13514,11701449166,670,3290,2,4,817,31175067
%N A212615 Least k > 1 such that the product pen(n) * pen(k) is pentagonal, or zero if no such k exists, where pen(k) is the k-th pentagonal number.
%C A212615 That is, pen(k) = k*(3k-1)/2.
%e A212615 For n = 2, pen(n) = 5 and the first k is 39 because pen(39) = 2262 and 5*2262 = 11310 which is the 87th pentagonal number.
%t A212615 kMax = 10^7; PentagonalQ[n_] := IntegerQ[(1 + Sqrt[1 + 24*n])/6]; Table[t = n*(3*n - 1)/2; k = 2; While[t2 = k*(3*k - 1)/2; k < kMax && ! PentagonalQ[t*t2], k++]; If[k == kMax, 0, k], {n, 15}]
%Y A212615 Cf. A188663 (pentagonal numbers that are pen(x) * pen(y) for some x,y > 1).
%Y A212615 Cf. A212614 (similar sequence for triangular numbers).
%Y A212615 Cf. A000326 (pentagonal numbers).
%K A212615 nonn
%O A212615 1,1
%A A212615 _T. D. Noe_, Jun 07 2012
%E A212615 a(25) corrected and a(28)-a(42) from _Donovan Johnson_, Feb 08 2013