A271186 Odd integers k such that k^k + 1 is the sum of 2 nonzero squares.

1, 9, 17, 25, 49, 73, 81, 89, 97, 121

Offset: 1

Author

Altug Alkan, Apr 01 2016

Keywords

• nonn
• more

Examples

			9 is a term because 9^9 + 1 = 1457^2 + 19629^2.
		

Crossrefs

Cf. A000404, A014566.

Programs

Mathematica

Select[Range[1, 25, 2], Length[PowersRepresentations[#^# + 1, 2, 2] /. {0, } -> Nothing] > 0 &] (* _Michael De Vlieger, Apr 01 2016 *)

PARI

a014566(n) = n^n+1;
isA000404(n) = { for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
for(n=1, 1e2, if(isA000404(a014566(n)) && n%2 == 1, print1(n, ", ")));

Extensions

a(6)-a(10) from Jinyuan Wang, Aug 14 2022