

A080131


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


4



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

1,1


COMMENTS

Primes that are the sum of consecutive integers (k=0) and consecutive squares (k=1) 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) = 3 because there are three Fermat primes (with k>1): 17, 257, 65537.


MATHEMATICA

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


CROSSREFS

Cf. A019434, A078902, A080133, A080134.
Sequence in context: A230500 A010281 A298421 * A319956 A082882 A188902
Adjacent sequences: A080128 A080129 A080130 * A080132 A080133 A080134


KEYWORD

nonn,hard,more


AUTHOR

T. D. Noe, Jan 30 2003


STATUS

approved



