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A080134 Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>=0. 6
5, 3, 3, 2, 4, 3, 2, 3, 3, 1, 1, 3, 1, 4, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

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) = 5 because there are five known Fermat primes: 3, 5, 17, 257, 65537.

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

CROSSREFS

Cf. A019434, A078902, A080131, A080133.

Sequence in context: A068118 A076104 A094284 * A057435 A246728 A155685

Adjacent sequences:  A080131 A080132 A080133 * A080135 A080136 A080137

KEYWORD

nonn,hard,more

AUTHOR

T. D. Noe, Jan 30 2003

STATUS

approved

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Last modified October 14 06:51 EDT 2019. Contains 327995 sequences. (Running on oeis4.)