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%I #3 Apr 03 2023 10:36:11
%S 3,5,37,41,43,59,71,113,181,293,383,421,1109,1187,1997,3109,4889,5581,
%T 67961,74843
%N Numbers n such that (x^n-1/x^n)/(x-1/x) is prime, where x = sqrt(3) + sqrt(2)
%C 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.
%H Prime Pages, <a href="https://t5k.org/top20/page.php?id=47">Lehmer number</a>
%e 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.
%K nonn
%O 1,1
%A _David Broadhurst_, Mar 28 2009
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