A217551 Smallest numbers n, for a given s, such that s! + n^2 and (s+3)! + n^2 are squares.

1, 828, 508, 239499435, 4693095288000, 561589459200, 148245349824000

Offset

1,2

Comments

The corresponding values of s are: 4, 8, 9, 15, 21, 24, 27.

Links

Table of n, a(n) for n=1..7.

Example

4! + 1 = 5^2 and 7! + 1 = 71^2.
8! + 828^2 = 852^2 and 11! + 828^2 = 6372^2.

Prog

(PARI) for(n=4, 30, a=n!; b=((n+3)*(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: A340115 A134726 A104281 * A179169 A260013 A234085

Adjacent sequences: A217548 A217549 A217550 * A217552 A217553 A217554

Keyword

nonn

Author

Robin Garcia, Oct 06 2012

Status

approved