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

1,1

Comments

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

Links

Table of n, a(n) for n=1..42.

Example

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.

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}]

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).

Sequence in context: A352021 A177773 A274574 * A247878 A339774 A232086

Adjacent sequences: A212612 A212613 A212614 * A212616 A212617 A212618

Keyword

nonn

Author

T. D. Noe, Jun 07 2012

Extensions

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

Status

approved