A119563 Define F(n) = 2^(2^n)+1 = n-th Fermat number, M(n) = 2^n-1 = the n-th Mersenne number. Then a(n) = F(n)+M(n)-1 = 2^(2^n) + 2^n - 1.

2, 5, 19, 263, 65551, 4294967327, 18446744073709551679, 340282366920938463463374607431768211583, 115792089237316195423570985008687907853269984665640564039457584007913129640191

Offset: 0

Author

Cino Hilliard, May 31 2006

Keywords

• nonn

Comments

The first 5 entries are primes. Are there infinitely many primes in this sequence?

Examples

			F(2) = 2^(2^2)+1 = 17, M(2) = 2^2-1 = 3, F(2)+ M(2) - 1 = 19
		

Programs

PARI

fm3(n) = for(x=0,n,y=2^(2^x)+2^x-1;print1(y","))

Formula

a(n) = A119561(n)-2=A000215(n)+A000225(n)-1. - R. J. Mathar, Apr 22 2007

Extensions

Edited by N. J. A. Sloane, Jun 03 2006