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A051154 1 + 2^k + 4^k where k = 3^n. 7
7, 73, 262657, 18014398643699713, 5846006549323611672814741748716771307882079584257 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

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.

LINKS

Table of n, a(n) for n=0..4.

D. Alpern, Factors of Generalized Fermat Numbers

FORMULA

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

MAPLE

with(numtheory); 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

Cf. A001576, A051155-A051157.

Sequence in context: A258379 A134281 A215612 * A172257 A106427 A106417

Adjacent sequences:  A051151 A051152 A051153 * A051155 A051156 A051157

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 24 02:10 EDT 2017. Contains 283984 sequences.