OFFSET
0,1
COMMENTS
The first three terms are prime. Are there more? Golomb shows that k must be a power of 3 in order for 1 + 2^k + 4^k to be prime. - T. D. Noe, Jul 16 2008
The next term, a(5) has 147 digits and is too large to include in DATA. - David A. Corneth, Aug 19 2020
LINKS
Jeppe Stig Nielsen, Table of n, a(n) for n = 0..6
Dario Alpern, Factors of Generalized Fermat Numbers
Walter Feit, Finite projective planes and a question about primes, Proc. AMS, Vol. 108(1990), 561-564.
Solomon W. Golomb, Cyclotomic polynomials and factorization theorems, Amer. Math. Monthly 85 (1978), 734-737.
FORMULA
a(n) = (2^(3^(n+1))-1)/(2^(3^n)-1).
MAPLE
F:= proc(n, r) local p; p := ithprime(r); (2^(p^(n+1))-1)/(2^(p^n)-1); end:
[ seq(F(n, 2), n=0..5) ];
MATHEMATICA
Table[4^(3^n) + 2^(3^n) + 1, {n, 1, 5}] (* Artur Jasinski, Oct 31 2011 *)
PROG
(PARI) a(n)=1+2^3^n+4^3^n \\ Charles R Greathouse IV, Oct 31 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved