

A080134


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


6



5, 3, 3, 2, 4, 3, 2, 3, 3, 1, 1, 3, 1, 4, 1, 1
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OFFSET

1,1


COMMENTS

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.


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) = 5 because there are five known Fermat primes: 3, 5, 17, 257, 65537.


MATHEMATICA

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


CROSSREFS

Cf. A019434, A078902, A080131, A080133.
Sequence in context: A068118 A076104 A094284 * A057435 A246728 A155685
Adjacent sequences: A080131 A080132 A080133 * A080135 A080136 A080137


KEYWORD

nonn,hard,more


AUTHOR

T. D. Noe, Jan 30 2003


STATUS

approved



