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Search: id:A051154
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| A051154 |
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a(n) = 1 + 2^k + 4^k where k = 3^n. |
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+0
6
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| 7, 73, 262657, 18014398643699713, 5846006549323611672814741748716771307882079584257, 19979190722022350280842222270676264356791028113055815365498604541602379129859977\ 6205926665232729866160172271718389895040313622108447299869943529473
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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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 (noe(AT)sspectra.com), 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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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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CROSSREFS
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Cf. A001576, A051155-A051157.
Sequence in context: A048174 A058350 A134281 this_sequence A106427 A106417 A137141
Adjacent sequences: A051151 A051152 A051153 this_sequence 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 (njas(AT)research.att.com).
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