A066857 Smallest number k such that n! - k is a square.

0, 1, 2, 8, 20, 44, 140, 320, 476, 3584, 12311, 4604, 74879, 414119, 2071775, 5703551, 11551671, 45680444, 442548224, 1960632176, 2657058876, 24923993276, 130518272975, 1478154932316, 5446454455004, 38610655379975

Offset: 1

Author

Reinhard Zumkeller, Jan 21 2002

Keywords

• nonn

Comments

Sequence is not monotonic: a(n) < a(n-1) for n = 12, 71, 90, 143, 145, 151, 172, 218, 257. - Zak Seidov, Jun 25 2013

Examples

			a(10) = 3628800 - 1904 * 1904 = 3628800 - 3625216 = 3584.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A068869.

Programs

Mathematica

Table[n! - Floor[Sqrt[n! ]]^2, {n, 1, 27}]

PARI

a(n)=my(N=n!); N-sqrtint(N)^2 \\ Charles R Greathouse IV, Jun 25 2013

Formula

a(n) = A053186(n!) = n!-A048760(n!) = n!-floor(sqrt(n!))^2 = n!-A055226(n)^2.

Extensions

More terms from Vladeta Jovovic, Mar 21 2002

Edited by Robert G. Wilson v and N. J. A. Sloane, Mar 22 2002