A080131 Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>1.

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

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

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

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

Cf. A019434, A078902, A080133, A080134.

Sequence in context: A010281 A353361 A298421 * A319956 A082882 A188902

Adjacent sequences: A080128 A080129 A080130 * A080132 A080133 A080134

Keyword

nonn,hard,more

Author

T. D. Noe, Jan 30 2003

Status

approved