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A158878 Numbers n such that (x^n-1/x^n)/(x-1/x) is prime, where x = sqrt(3) + sqrt(2) 0
3, 5, 37, 41, 43, 59, 71, 113, 181, 293, 383, 421, 1109, 1187, 1997, 3109, 4889, 5581, 67961, 74843 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 8 23:03 EST 2023. Contains 360153 sequences. (Running on oeis4.)