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A158892
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Numbers k such that (x^k + 1/x^k)/(x + 1/x) is prime, where x = sqrt(3) + sqrt(2).
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1
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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David Broadhurst and others, The house that Jack built, digest of 69 messages in primenumbers Yahoo group, Mar 22 - May 10, 2009.
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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