A264890 Integers k such that k! + 1 is the sum of 2 nonzero squares.

0, 1, 4, 8, 11, 12, 17, 25, 26, 27, 28, 29, 37, 38, 41, 45, 48, 54, 60, 67, 71, 73, 75, 77, 88, 92, 94, 114, 115, 116, 119, 133

Offset

1,3

Links

Table of n, a(n) for n=1..32.

Example

a(3) = 4 because 4! + 1 = 4^2 + 3^2.

Mathematica

Flatten@ Position[Map[Length, Map[Map[Length, PowersRepresentations[#, 2, 2] &@(#! + 1) /. 0 -> Nothing] &, Range[0, 48]] /. 1 -> Nothing], n_ /; n > 0] - 1 (* Michael De Vlieger, Nov 28 2015 *)

Prog

(PARI) is(n) = { for(i=1, #n=factor(n!+1)~%4, n[1, i]==3 && n[2, i]%2 && return); n && (vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)) }

Crossrefs

Cf. A000404, A038507, A264665, A271186.

Sequence in context: A288150 A311019 A068798 * A272299 A282144 A147515

Adjacent sequences: A264887 A264888 A264889 * A264891 A264892 A264893

Keyword

nonn,more

Author

Altug Alkan, Nov 27 2015

Extensions

a(25)-a(32) from Jinyuan Wang, May 22 2021

Status

approved