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A080134
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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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6
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5, 3, 3, 2, 4, 3, 2, 3, 3, 1, 1, 3, 1, 4, 1, 1
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OFFSET
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1,1
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COMMENTS
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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. The next n>1 for which (n+1)^2^k + n^2^k is prime for k=0,1,2,3,4 is n=826284.
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LINKS
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EXAMPLE
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a(1) = 5 because there are five known Fermat primes: 3, 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, 0, 16}]; AppendTo[lst, prms], {n, 16}]; lst
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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