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Search: id:A080133
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| A080133 |
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Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>0. |
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3
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| 4, 2, 2, 2, 3, 2, 2, 2, 2, 1, 0, 3, 1, 3, 0, 1
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Primes that are the sum of consecutive integers (k=0) are excluded. Values of k <= 16 were tested. The sequence A078902 lists some of the generalized Fermat primes. Bjorn and Riesel examined generalized Fermat numbers for n <= 11 and k <= 999.
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REFERENCES
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A. Bjorn and H. Riesel, "Factors of generalized Fermat numbers," Math. Comp., 67 (1998) 441-446.
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LINKS
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Eric Weisstein's World of Mathematics, Generalized Fermat Number
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EXAMPLE
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a(1) = 4 because there are four known Fermat primes (with k>0): 5, 17, 257, 65537.
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MATHEMATICA
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lst={}; Do[prms=0; Do[If[PrimeQ[(n+1)^2^k+n^2^k], prms++ ], {k, 1, 16}]; AppendTo[lst, prms], {n, 16}]; lst
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CROSSREFS
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Cf. A019434, A078902, A080131, A080134.
Sequence in context: A137239 A136714 A010314 this_sequence A054575 A129107 A058634
Adjacent sequences: A080130 A080131 A080132 this_sequence A080134 A080135 A080136
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KEYWORD
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hard,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 30 2003
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