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A260374 The distance between n! and the nearest perfect square. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 8 00:42 EST 2023. Contains 360133 sequences. (Running on oeis4.)