

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
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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 = gs**2
....A260374_list.append(int(t if ts <= 0 else 2*s+1t)) # Chai Wah Wu, Jul 23 2015


CROSSREFS

Cf. A260373, A260375.
Sequence in context: A165889 A087127 A144946 * 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



