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

Author

Robin Garcia, Oct 06 2012

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

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

Programs

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