A080133 Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>0.

4, 2, 2, 2, 3, 2, 2, 2, 2, 1, 0, 3, 1, 3, 0, 1

Offset: 1

Author

T. D. Noe, Jan 30 2003

Keywords

• nonn
• hard
• more

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.

Examples

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

Links

• 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

Crossrefs

Cf. A019434, A078902, A080131, A080134.

Programs

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