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.

2, 39, 2231, 40, 14, 94974, 47, 212, 1071, 477, 124, 261, 15120, 5, 180, 375638, 2413, 22, 4270831, 924, 278, 18, 126, 33510, 355, 376, 9047610, 37313170, 1533015, 7315, 1687018, 520, 363155, 8827, 13514, 11701449166, 670, 3290, 2, 4, 817, 31175067

Offset: 1

Author

T. D. Noe, Jun 07 2012

Keywords

• nonn

Comments

That is, pen(k) = k*(3k-1)/2.

Examples

			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.
		

Crossrefs

Cf. A188663 (pentagonal numbers that are pen(x) * pen(y) for some x,y > 1).

Cf. A212614 (similar sequence for triangular numbers).

Cf. A000326 (pentagonal numbers).

Programs

Mathematica

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}]

Extensions

a(25) corrected and a(28)-a(42) from Donovan Johnson, Feb 08 2013