A119550 Prime numbers of the form 2^(2^k) + 2^k - 1.

2, 5, 19, 263, 65551

Offset: 1

Author

Cino Hilliard, May 31 2006

Keywords

• nonn
• more
• less

Examples

			F(2)= 2^(2^2)+1 = 17, M(2) = 2^2-1 = 3, F(2)+ M(2)-1 = 19 is prime, so 2 is a member.
		

Crossrefs

Cf. A119563, A119564.

Programs

Mathematica

Select[Table[2^(2^k)+2^k-1,{k,0,10}],PrimeQ] (* James C. McMahon, Sep 15 2024 *)

PARI

fmp3(n)=for(x=0,n,y=2^(2^x)+2^x-1;if(ispseudoprime(y),print1(y",")))

Formula

Define F(n) = 2^(2^n)+1 = n-th Fermat number, M(n) = 2^n-1 = the n-th Mersenne number. Then we are considering the numbers f(n) = F(n)+M(n)-1 = 2^(2^n) + 2^n - 1 (cf. A119563).

Extensions

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

Definition corrected by Stefan Steinerberger, Jun 10 2007