A260373 - OEIS

%I #16 Jul 24 2015 20:52:02

%S 1,1,1,4,25,121,729,5041,40401,362404,3629025,39917124,478996996,

%T 6226945921,87178467600,1307674583296,20922793332736,355687416544329,

%U 6402373660047556,121645100663836929,2432902009335560361,51090942169052381124,1124000727752683686724

%N The nearest perfect square to n!

%C 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

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

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

%o (PARI) a(n)=round(sqrt(n!))^2 \\ _Charles R Greathouse IV_, Jul 23 2015

%o (Python)

%o from gmpy2 import isqrt

%o A260373_list, g = [1], 1

%o for i in range(1, 101):

%o ....g *= i

%o ....s = isqrt(g)

%o ....t = s**2

%o ....A260373_list.append(int(t if g-t-s <= 0 else t+2*s+1)) # _Chai Wah Wu_, Jul 23 2015

%Y Cf. A055227, A260374.

%K nonn,easy

%O 0,4

%A _Otis Tweneboah_, _Pratik Koirala_, _Eugene Fiorini_, _Nathan Fox_, Jul 23 2015