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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 LINKS D. 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 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, A051156, A051157. Sequence in context: A134281 A215612 A292012 * A172257 A106427 A106417 Adjacent sequences:  A051151 A051152 A051153 * A051155 A051156 A051157 KEYWORD nonn AUTHOR STATUS approved

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