

A080208


a(n) is the least k such that the generalized Fermat number (k+1)^(2^n) + k^(2^n) is prime.


5



1, 1, 1, 1, 1, 8, 95, 31, 85, 59, 1078, 754, 311, 3508, 1828, 49957, 22844
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OFFSET

0,6


COMMENTS

The first five terms correspond to the five known Fermat primes. The sequence A078902 lists some of the generalized Fermat primes. Bjorn and Riesel examined generalized Fermat numbers for k <= 11 and n <= 999. The sequence A080134 lists the conjectured number of primes for each k.
For n >= 10, a(n) yields a probable prime. a(13) was found by Henri Lifchitz. It is known that a(14) > 1000.


LINKS



FORMULA



EXAMPLE

a(5) = 8 because (k+1)^32 + k^32 is prime for k = 8 and composite for k < 8.


CROSSREFS



KEYWORD

hard,more,nonn


AUTHOR



EXTENSIONS



STATUS

approved



