login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A080131 Conjectured number of generalized Fermat primes of the form (n+1)^2^k + n^2^k, with k>1. 4
3, 1, 2, 1, 2, 2, 1, 2, 1, 1, 0, 2, 1, 2, 0, 1 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A010281 A353361 A298421 * A319956 A082882 A188902
KEYWORD
nonn,hard,more
AUTHOR
T. D. Noe, Jan 30 2003
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 2 10:39 EST 2024. Contains 370466 sequences. (Running on oeis4.)