

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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.


REFERENCES

A. Bjorn and H. Riesel, "Factors of generalized Fermat numbers," Math. Comp., 67 (1998) 441446.


LINKS

Table of n, a(n) for n=1..16.
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

hard,nonn


AUTHOR

T. D. Noe, Jan 30 2003


STATUS

approved



