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

0,4

Links

Table of n, a(n) for n=0..29.

Formula

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

Example

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

Prog

(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

Crossrefs

Cf. A260373, A260375.

Sequence in context: A087127 A144946 A332717 * A157109 A185814 A174553

Adjacent sequences: A260371 A260372 A260373 * A260375 A260376 A260377

Keyword

nonn

Author

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

Status

approved