A080134 Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>=0.

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

Offset: 1

Author

T. D. Noe, Jan 30 2003

Keywords

• nonn
• hard
• more

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.

Examples

			a(1) = 5 because there are five known Fermat primes: 3, 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, A080133.

Programs

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