OFFSET
1,1
COMMENTS
This does not count x^2 and (-x)^2 as distinct, nor does it count 0! and 1! as distinct.
For any two factorials a > b, where a-b = m*n where m > n and (m and n are both even or m and n are both odd), (((m-n)/2)^2 + a) will appear in this sequence.
EXAMPLE
145 = 5^2 + 5! = 11^2 + 4! = 12^2 + 1!.
MATHEMATICA
With[{f = Range[8]!}, c[n_] := Count[f, _?(IntegerQ @ Sqrt[n - #] &)]; Select[Range[f[[-1]]], c[#] > 1 &]] (* Amiram Eldar, Oct 30 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Walter Robinson, Oct 30 2022
STATUS
approved