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A051154 1 + 2^k + 4^k where k = 3^n. 7

%I

%S 7,73,262657,18014398643699713,

%T 5846006549323611672814741748716771307882079584257

%N 1 + 2^k + 4^k where k = 3^n.

%C 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

%H D. Alpern, <a href="http://www.alpertron.com.ar/MODFERM.HTM">Factors of Generalized Fermat Numbers</a>

%H Walter Feit, <a href="https://doi.org/10.1090/S0002-9939-1990-1002157-4">Finite projective planes and a question about primes</a>, Proc. AMS, Vol. 108(1990), 561-564.

%H Solomon W. Golomb, <a href="http://www.jstor.org/stable/2321679">Cyclotomic polynomials and factorization theorems</a>, Amer. Math. Monthly 85 (1978), 734-737.

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

%p 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) ];

%t Table[4^(3^n) + 2^(3^n) + 1, {n, 1, 5}] (* Artur Jasinski, Oct 31 2011 *)

%o (PARI) a(n)=1+2^3^n+4^3^n \\ _Charles R Greathouse IV_, Oct 31 2011

%Y Cf. A001576, A051155, A051156, A051157.

%K nonn

%O 0,1

%A _N. J. A. Sloane_.

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Last modified February 21 01:15 EST 2019. Contains 320364 sequences. (Running on oeis4.)