A136116 Indices of pentagonal numbers (A000326) which are the sum of 2 other positive pentagonal numbers.

7, 8, 24, 25, 29, 31, 36, 42, 49, 59, 65, 66, 69, 72, 73, 74, 76, 80, 83, 93, 94, 99, 102, 104, 110, 117, 118, 121, 122, 123, 124, 126, 127, 138, 140, 144, 149, 150, 152, 161, 163, 168, 169, 174, 175, 178, 181, 185, 188, 190, 195, 199, 203, 209, 210, 212, 213

Offset

1,1

Links

Table of n, a(n) for n=1..57.

Formula

A000326(a(n))=A000326(m)+A136114(m) where m is the index of the n-th nonzero term in A136114 or A136115.

Example

a(1)=7 since P(7)=70 is the least pentagonal number which can be written as sum of two other pentagonal numbers, P(7)=P(5)+P(5).

Prog

(PARI) P(n)=n*(3*n-1)>>1 /* a.k.a. A000326 */
isPent(t)=P(sqrtint(t<<1\3)+1)==t
for(i=1, 999, for(j=1, (i+1)\sqrt(2), isPent(P(i)-P(j))&print1(i", ") || next(2)))
/* The following are much faster, at the cost of implementing sum2sqr(), cf. A133388. */
A136116next(i)=i=6*i-1; until(0, for(j=2, #t=sum2sqr((i+=6)^2+1), t[j]%6==[5, 5] && break(2))); i\6+1
A136116vect(n, i=0)=vector(n, j, i=A136116next(i))
A136116(n, i=0)=until(!n--, i=A136116next(i)); i \\ M. F. Hasler, Dec 25 2007

Crossrefs

Cf. A000326, A136112-A136118.

Sequence in context: A042391 A042023 A041102 * A329635 A376007 A080982

Adjacent sequences: A136113 A136114 A136115 * A136117 A136118 A136119

Keyword

nonn

Author

M. F. Hasler, Dec 15 2007; corrected Dec 25 2007

Status

approved