

A158892


Numbers k such that (x^k + 1/x^k)/(x + 1/x) is prime, where x = sqrt(3) + sqrt(2).


1




OFFSET

1,1


COMMENTS

The Lehmer number (x^n + 1/x^n)/(x + 1/x), with x = sqrt(3) + sqrt(2), may be prime only if the index n is prime. For the listed indices up to n = 491, the Lehmer number is prime; thereafter it is a probable prime.
The Lehmer number with index n = 8009 is known to be prime  see the Yahoo link.  David Broadhurst, Mar 30 2009


LINKS

Table of n, a(n) for n=1..9.
David Broadhurst and others, The house that Jack built, digest of 69 messages in primenumbers Yahoo group, Mar 22  May 10, 2009.
Prime Pages, Lehmer number


EXAMPLE

a(3) = 13 since ((sqrt(3) + sqrt(2))^13 + (sqrt(3)  sqrt(2))^13)/(2*sqrt(3)) = 854569 is the third prime in this Lehmer sequence.


CROSSREFS

Sequence in context: A102872 A102873 A342506 * A106022 A279795 A050085
Adjacent sequences: A158889 A158890 A158891 * A158893 A158894 A158895


KEYWORD

nonn,more


AUTHOR

David Broadhurst, Mar 29 2009


STATUS

approved



