

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 kth pentagonal number.


1



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
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OFFSET

1,1


COMMENTS

That is, pen(k) = k*(3k1)/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: A245053 A177773 A274574 * A247878 A232086 A047660
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



