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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 g-t-s <= 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

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)