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

1,3

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

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A068869.

Sequence in context: A296954 A203604 A240940 * A146168 A058405 A133326

Adjacent sequences: A066854 A066855 A066856 * A066858 A066859 A066860

Keyword

nonn

Author

Reinhard Zumkeller, Jan 21 2002

Extensions

More terms from Vladeta Jovovic, Mar 21 2002

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

Status

approved