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

Author

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

Keywords

• nonn

Examples

			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).
		

Crossrefs

Cf. A000326, A136112-A136118.

Programs

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

Formula

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