A051154 a(n) = 1 + 2^k + 4^k where k = 3^n.

7, 73, 262657, 18014398643699713, 5846006549323611672814741748716771307882079584257

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A001576, A051155, A051156, A051157.

Programs

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 *)

PARI

a(n)=1+2^3^n+4^3^n \\ Charles R Greathouse IV, Oct 31 2011

Formula

a(n) = (2^(3^(n+1))-1)/(2^(3^n)-1).