A136114 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, 70, 0, 0, 782, 0, 0, 3432, 0, 715, 10045, 3290, 0, 23375, 1001, 0, 715, 2035, 7526, 84847, 0, 0, 1001, 41251, 0, 4030, 64170, 32340, 20475, 14652, 11310, 490490, 7740, 6700, 5922, 190995, 4845, 18095, 259376, 3876, 1260875, 10045, 3290

Offset

1,4

Links

Table of n, a(n) for n=1..45.

Formula

a(n)=A000326(A136115(n)). 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)=70=P(7) 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(P(j)", ")|next(2)); print1(0", "))

Crossrefs

Cf. A000326, A136112-A136118.

Sequence in context: A175049 A116099 A116238 * A365913 A278074 A075405

Adjacent sequences: A136111 A136112 A136113 * A136115 A136116 A136117

Keyword

nonn

Author

M. F. Hasler, Dec 15 2007

Status

approved