OFFSET
1,1
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).
EXAMPLE
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.
MATHEMATICA
Select[Table[2^(2^k)+2^k-1, {k, 0, 10}], PrimeQ] (* James C. McMahon, Sep 15 2024 *)
PROG
(PARI) fmp3(n)=for(x=0, n, y=2^(2^x)+2^x-1; if(ispseudoprime(y), print1(y", ")))
CROSSREFS
KEYWORD
nonn,more,less
AUTHOR
Cino Hilliard, May 31 2006
EXTENSIONS
Edited by N. J. A. Sloane, Jun 03 2006
Definition corrected by Stefan Steinerberger, Jun 10 2007
STATUS
approved