A158878 Numbers n such that (x^n-1/x^n)/(x-1/x) is prime, where x = sqrt(3) + sqrt(2)

3, 5, 37, 41, 43, 59, 71, 113, 181, 293, 383, 421, 1109, 1187, 1997, 3109, 4889, 5581, 67961, 74843

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 = 1997 the Lehmer number is prime; thereafter it is a probable prime.

Links

Table of n, a(n) for n=1..20.

Prime Pages, Lehmer number

Example

a(3) = 37 since ((sqrt(3)+sqrt(2))^37-(sqrt(3)-sqrt(2))^37)/(2*sqrt(2)) = 926569189346784589 is the third prime in this Lehmer sequence.

Crossrefs

Sequence in context: A145640 A222496 A086158 * A337858 A337859 A184314

Adjacent sequences: A158875 A158876 A158877 * A158879 A158880 A158881

Keyword

nonn

Author

David Broadhurst, Mar 28 2009

Status

approved