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
Keywords
Examples
6!=720. The nearest perfect square is 729. The difference between these is 9, so a(6)=9.
Programs
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PARI
a(n)=abs(n!-round(sqrt(n!))^2) \\ Charles R Greathouse IV, Jul 23 2015
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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)).