

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



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



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



