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A051154
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1 + 2^k + 4^k where k = 3^n.
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6
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..4.
D. Alpern, Factors of Generalized Fermat Numbers
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FORMULA
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a(n) = (2^(3^(n+1))-1)/(2^(3^n)-1).
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MAPLE
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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) ];
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MATHEMATICA
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Table[4^(3^n) + 2^(3^n) + 1, {n, 1, 5}] (* Artur Jasinski Oct 31 2011 *)
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PROG
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(PARI) a(n)=1+2^3^n+4^3^n \\ Charles R Greathouse IV, Oct 31 2011
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CROSSREFS
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Cf. A001576, A051155-A051157.
Sequence in context: A048174 A134281 A215612 * A172257 A106427 A106417
Adjacent sequences: A051151 A051152 A051153 * A051155 A051156 A051157
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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