A136115 Index m of least pentagonal number P(m) > P(n) such that P(m)+P(n) is again a pentagonal number, 0 if no such m exists.

0, 0, 0, 7, 0, 0, 23, 0, 0, 48, 0, 22, 82, 47, 0, 125, 26, 0, 22, 37, 71, 238, 0, 0, 26, 166, 0, 52, 207, 147, 117, 99, 87, 572, 72, 67, 63, 357, 57, 110, 416, 51, 917, 82, 47, 1050, 217, 380, 167, 246, 0, 97, 697, 0, 374, 191, 537, 1672, 152, 112, 136, 380, 215, 2037, 68

Offset

1,4

Links

Table of n, a(n) for n=1..65.

Formula

a(n)=0 iff n is in A136112 iff A000326(n) is in A136113.

Example

a(1..3)=0 since P(1),P(2),P(3) cannot be written as difference of 2 other pentagonal numbers > 0.
a(4)=7 since P(7)=70 is the least pentagonal number > P(4)=22 such that their sum is again a pentagonal number, P(8).

Prog

(PARI) P(n)=n*(3*n-1)>>1 /* a.k.a. A000326 */ /* newline */ isPent(t)=P(sqrtint(t<<1\3)+1)==t /* newline */ for(i=1, 99, for(j=i+1, (P(i)-1)\3, isPent(P(i)+P(j))&print1(j", ")|next(2)); print1(0", "))

Crossrefs

Cf. A000326, A136112-A136118.

Sequence in context: A094898 A341806 A340906 * A061846 A335947 A293530

Adjacent sequences: A136112 A136113 A136114 * A136116 A136117 A136118

Keyword

nonn

Author

M. F. Hasler, Dec 15 2007

Status

approved