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Search: id:A158878
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| A158878 |
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Numbers n such that (x^n-1/x^n)/(x-1/x) is prime, where x = sqrt(3) + sqrt(2) |
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+0
1
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| 3, 5, 37, 41, 43, 59, 71, 113, 181, 293, 383, 421, 1109, 1187, 1997, 3109, 4889, 5581, 67961, 74843
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OFFSET
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1,1
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COMMENT
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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 = 1997 the Lehmer number is prime; thereafter it is a probable prime.
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LINKS
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Prime Pages, Lehmer number
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A077784 A145640 A086158 this_sequence A077779 A146318 A145912
Adjacent sequences: A158875 A158876 A158877 this_sequence A158879 A158880 A158881
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KEYWORD
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nonn
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AUTHOR
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David Broadhurst (D.Broadhurst(AT)open.ac.uk), Mar 28 2009
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