A085602 Numbers of the form (2n+1)^(2n+1) + 1.

2, 28, 3126, 823544, 387420490, 285311670612, 302875106592254, 437893890380859376, 827240261886336764178, 1978419655660313589123980, 5842587018385982521381124422, 20880467999847912034355032910568, 88817841970012523233890533447265626

Offset: 1

Author

Cino Hilliard, Jul 07 2003

Keywords

• easy
• nonn

Comments

Also even Sierpinski numbers of the first kind.

No term is a square. Moreover, x^x + 1 != k^x, for if it were, we would have a counterexample to Fermat's Last Theorem.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..193

Crossrefs

Bisection of A014566 (odd part).

Programs

Mathematica

#^#+1&/@Range[1,21,2] (* Harvey P. Dale, Dec 08 2012 *)

PARI

forstep(x=1,20,2,print1(x^x+1" "))

Formula

a(n) = (2*n-1)^(2*n-1)+1. - Alois P. Heinz, Feb 27 2020