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A088790
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Numbers k such that (k^k-1)/(k-1) is prime.
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9
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OFFSET
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1,1
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COMMENTS
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Note that (k^k-1)/(k-1) is prime only if k is prime, in which case it equals cyclotomic(k,k), the k-th cyclotomic polynomial evaluated at x=k. This sequence is a subsequence of A070519. The number cyclotomic(7547,7547) is a probable prime found by H. Lifchitz. Are there only a finite number of these primes?
From T. D. Noe, Dec 16 2008: (Start)
The standard heuristic implies that there are an infinite number of these primes and that the next k should be between 10^10 and 10^11.
Let N = (7547^7547-1)/(7547-1) = A023037(7547). If N is prime, then the period of the Bell numbers modulo 7547 is N. See A054767. (End)
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REFERENCES
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R. K. Guy, Unsolved Problems in Theory of Numbers, 1994, A3.
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LINKS
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Table of n, a(n) for n=1..5.
Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature.
Eric Weisstein's World of Mathematics, Cyclotomic Polynomial
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MATHEMATICA
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Do[p=Prime[n]; If[PrimeQ[(p^p-1)/(p-1)], Print[p]], {n, 100}]
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PROG
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(PARI) is(n)=ispseudoprime((n^n-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017
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CROSSREFS
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Cf. A070519 (cyclotomic(n, n) is prime).
Cf. A056826 ((n^n+1)/(n+1) is prime).
Sequence in context: A040145 A142955 A213896 * A283186 A215304 A215281
Adjacent sequences: A088787 A088788 A088789 * A088791 A088792 A088793
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KEYWORD
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hard,more,nonn
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AUTHOR
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T. D. Noe, Oct 16 2003
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STATUS
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approved
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