A230365 Squares representable as b! + triangular(c).

1, 4, 9, 16, 25, 121, 144, 196, 225, 256, 324, 441, 529, 900, 1296, 4096, 4489, 5041, 5476, 6561, 7056, 10609, 14884, 15625, 17956, 28561, 42025, 44100, 46656, 53361, 136900, 139129, 143641, 152100, 184041, 220900, 222784, 360000, 370881, 404496, 443556, 505521, 609961

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Prog

(Python)
import math
factorials = [1] * 1024
f = 1
for n in range(2, 1025):
    f *= n
    factorials[n-1] = f
for n in range(1<<30):
    t = n*n
    for a in factorials:
        r = t - a
        if r<0: break
        b = int(math.sqrt(2*r))
        if b*(b+1)==r*2:
            print(t, end=', ')
            break

Crossrefs

Cf. A000290, A000142, A000217.

Sequence in context: A299153 A133900 A143480 * A274963 A353387 A050461

Adjacent sequences: A230362 A230363 A230364 * A230366 A230367 A230368

Keyword

nonn

Author

Alex Ratushnyak, Oct 17 2013

Status

approved