|
| |
|
|
A088790
|
|
Numbers n such that (n^n-1)/(n-1) is prime.
|
|
5
| | |
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Note that (n^n-1)/(n-1) is prime only if n is prime, in which case it equals cyclotomic(n,n), the n-th cyclotomic polynomial evaluated at x=n. This sequence is a subset of A070519. The number cyclotomic(7547,7547) is a probable prime found by H. Lifchitz. Are there only a finite number of these primes?
Contribution from T. D. Noe (noe(AT)sspectra.com), Dec 16 2008: (Start)
The standard heuristic implies that there are an infinite number of these primes and that the next n 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)
|
|
|
REFERENCES
| R. K. Guy, Unsolved Problems in Theory of Numbers, 1994, A3.
|
|
|
LINKS
| Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38.
Bernard Schott, Les nombres brésiliens, Reprinted from 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
|
|
|
MATHEMATICA
| Do[p=Prime[n]; If[PrimeQ[(p^p-1)/(p-1)], Print[p]], {n, 100}]
|
|
|
CROSSREFS
| Cf. A070519 (cyclotomic(n, n) is prime).
Cf. A056826 ((n^n+1)/(n+1) is prime).
Sequence in context: A058912 A040145 A142955 * A178202 A135958 A163665
Adjacent sequences: A088787 A088788 A088789 * A088791 A088792 A088793
|
|
|
KEYWORD
| hard,more,nonn
|
|
|
AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Oct 16 2003
|
| |
|
|
