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A158892 Numbers k such that (x^k + 1/x^k)/(x + 1/x) is prime, where x = sqrt(3) + sqrt(2). 1
5, 7, 13, 107, 227, 491, 8009, 36779, 80513 (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 = 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.
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
KEYWORD
nonn,more
AUTHOR
David Broadhurst, Mar 29 2009
STATUS
approved

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Last modified March 1 20:05 EST 2024. Contains 370443 sequences. (Running on oeis4.)