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

1,2

Links

Table of n, a(n) for n=1..10.

Example

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

Mathematica

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

Prog

(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, ", ")));

Crossrefs

Cf. A000404, A014566.

Sequence in context: A211432 A211422 A035198 * A253705 A056233 A260264

Adjacent sequences: A271183 A271184 A271185 * A271187 A271188 A271189

Keyword

nonn,more

Author

Altug Alkan, Apr 01 2016

Extensions

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

Status

approved