A260373 The nearest perfect square to n!

1, 1, 1, 4, 25, 121, 729, 5041, 40401, 362404, 3629025, 39917124, 478996996, 6226945921, 87178467600, 1307674583296, 20922793332736, 355687416544329, 6402373660047556, 121645100663836929, 2432902009335560361, 51090942169052381124, 1124000727752683686724

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 * A362391 A175733 A240479

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