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A119550
Prime numbers of the form 2^(2^k) + 2^k - 1.
1
2, 5, 19, 263, 65551
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
Sequence in context: A080280 A218386 A055813 * A119563 A270398 A269997
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