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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)



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.


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. 441-446.

Eric Weisstein's World of Mathematics, Generalized Fermat Number


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


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


Cf. A019434, A078902, A080131, A080134.

Sequence in context: A297825 A303577 A010314 * A054575 A129107 A255909

Adjacent sequences:  A080130 A080131 A080132 * A080134 A080135 A080136




T. D. Noe, Jan 30 2003



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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)