

A260373


The nearest perfect square to n!


3



1, 1, 1, 4, 25, 121, 729, 5041, 40401, 362404, 3629025, 39917124, 478996996, 6226945921, 87178467600, 1307674583296, 20922793332736, 355687416544329, 6402373660047556, 121645100663836929, 2432902009335560361, 51090942169052381124, 1124000727752683686724
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

a(n) is well defined as the squares are alternatingly odd and even and thus the average of two successive squares is not an integer and thus no integer is equidistant to two successive squares.  Chai Wah Wu, Jul 24 2015


LINKS

Table of n, a(n) for n=0..22.


FORMULA

a(n) = A055227(n)^2.


EXAMPLE

6! = 720. The nearest perfect square is 729.


PROG

(PARI) a(n)=round(sqrt(n!))^2 \\ Charles R Greathouse IV, Jul 23 2015
(Python)
from gmpy2 import isqrt
A260373_list, g = [1], 1
for i in range(1, 101):
....g *= i
....s = isqrt(g)
....t = s**2
....A260373_list.append(int(t if gts <= 0 else t+2*s+1)) # Chai Wah Wu, Jul 23 2015


CROSSREFS

Cf. A055227, A260374.
Sequence in context: A013187 A069639 A013582 * A175733 A240479 A317949
Adjacent sequences: A260370 A260371 A260372 * A260374 A260375 A260376


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



