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

Author

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

Keywords

• nonn
• easy

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

Examples

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

Crossrefs

Cf. A055227, A260374.

Programs

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

Formula

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