

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

David Broadhurst and others, The house that Jack built, digest of 69 messages in primenumbers Yahoo group, Mar 22  May 10, 2009.


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



KEYWORD

nonn,more


AUTHOR



STATUS

approved



