A260374 The distance between n! and the nearest perfect square.

0, 0, 1, 2, 1, 1, 9, 1, 81, 476, 225, 324, 4604, 74879, 176400, 215296, 3444736, 11551671, 45680444, 255004929, 1158920361, 2657058876, 24923993276, 130518272975, 97216010329, 2430400258225, 1553580508516, 4666092737476, 538347188396016, 2137864362693921

Offset: 0

Author

Otis Tweneboah, Pratik Koirala, Eugene Fiorini, Nathan Fox, Jul 23 2015

Keywords

• nonn

Examples

			6!=720. The nearest perfect square is 729. The difference between these is 9, so a(6)=9.
		

Crossrefs

Cf. A260373, A260375.

Programs

PARI

a(n)=abs(n!-round(sqrt(n!))^2) \\ Charles R Greathouse IV, Jul 23 2015

Python

from gmpy2 import isqrt
A260374_list, g = [0], 1
for i in range(1, 1001):
    g *= i
    s = isqrt(g)
    t = g-s**2
    A260374_list.append(int(t if t-s <= 0 else 2*s+1-t)) # Chai Wah Wu, Jul 23 2015

Formula

a(n) = abs(n!-A260373(n)).