A217550 Numbers n such that s! + n^2 and (s + 2)! + n^2 are squares for some s, ordered by s.

1, 179, 204, 108, 996, 2934, 81720, 2152080, 851040, 271106640, 7935621120, 1143137318400, 52250931532800

Offset

1,2

Comments

The corresponding numbers s are: 5, 6, 7, 8, 9, 11, 12, 14, 16, 17, 19, 25, 27.

Links

Table of n, a(n) for n=1..13.

Example

5! + 1 = 11^2 and 7! + 1 = 71^2.
6! + 179^2 = 181^2 and 8! + 179^2 = 269^2.
7! + 204^2 = 216^2 and 9! + 204^2 = 636^2.
8! + 108^2 = 228^2 and 10! + 108^2 = 1908^2.

Prog

(PARI) for(n=4, 32, a=n!; b=((n+2)*(n+1)-1)*a; c=divisors(b); for(i=2, #c-1, s=c[i]; r=b\s; if(r<s, next(2), d=abs(s-r)/2; t=d^2-a; if(issquare(t), print([n, d, sqrtint(t)])))))

Crossrefs

Cf. A217277, A217541, A217550, A217551, A217553.

Sequence in context: A053017 A140026 A108384 * A226928 A162164 A238893

Adjacent sequences: A217547 A217548 A217549 * A217551 A217552 A217553

Keyword

nonn

Author

Robin Garcia, Oct 06 2012

Status

approved