A158892 Numbers k such that (x^k + 1/x^k)/(x + 1/x) is prime, where x = sqrt(3) + sqrt(2).

5, 7, 13, 107, 227, 491, 8009, 36779, 80513

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: A102873 A356847 A342506 * A106022 A279795 A050085

Adjacent sequences: A158889 A158890 A158891 * A158893 A158894 A158895

Keyword

nonn,more

Author

David Broadhurst, Mar 29 2009

Status

approved