

A080133


Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>0.


2



4, 2, 2, 2, 3, 2, 2, 2, 2, 1, 0, 3, 1, 3, 0, 1
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OFFSET

1,1


COMMENTS

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.


LINKS

Table of n, a(n) for n=1..16.
Anders Björn and Hans Riesel, Factors of Generalized Fermat Numbers, Mathematics of Computation, Vol. 67, No. 221, Jan., 1998, pp. 441446.
Eric Weisstein's World of Mathematics, Generalized Fermat Number


EXAMPLE

a(1) = 4 because there are four known Fermat primes (with k>0): 5, 17, 257, 65537.


MATHEMATICA

lst={}; Do[prms=0; Do[If[PrimeQ[(n+1)^2^k+n^2^k], prms++ ], {k, 1, 16}]; AppendTo[lst, prms], {n, 16}]; lst


CROSSREFS

Cf. A019434, A078902, A080131, A080134.
Sequence in context: A137239 A136714 A010314 * A054575 A129107 A255909
Adjacent sequences: A080130 A080131 A080132 * A080134 A080135 A080136


KEYWORD

nonn,hard,more


AUTHOR

T. D. Noe, Jan 30 2003


STATUS

approved



