OFFSET
2,1
COMMENTS
When (n^k-1)/(n-1) is prime, k must be prime. As mentioned by Dubner, when n is a perfect power, then (n^k-1)/(n-1) will usually be composite for all k, which is the case for n = 9, 25, 32, 49, 64, 81, 121, 125, 144, 169, 216, 225, 243, 289, 324, 343, ... - T. D. Noe, Jan 30 2004
a(152) > prime(1100) or 0. - Derek Orr, Nov 29 2014
a(n)=2 if and only if n=p-1, where p is an odd prime; that is, n belongs to A006093, except 2. - Thomas Ordowski, Sep 19 2015
Probably a(152) = 270217 since (152^270217-1)/(152-1) has been shown to be probably prime. - Michael Stocker, Jan 24 2019
LINKS
Eric Chen, Table of known a(n) up to a(360) [with a(316) corrected by Jon E. Schoenfield]
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
Andy Steward, Titanic Prime Generalized Repunits
Eric Weisstein's World of Mathematics, Repunit
Robert G. Wilson v, Letter to N. J. A. Sloane, circa 1991.
Robert G. Wilson v, Table of known a(n) from n = 2 to 1000.
EXAMPLE
a(7) = 5 as (7^5 - 1 )/(7 - 1) = 2801 = 1 + 7 + 7^2 + 7^3 + 7^4 is a prime but no smaller partial sum yields a prime.
PROG
(PARI) a(n) = {l=List([9, 25, 32, 49, 64, 81, 121, 125, 144, 169, 216, 225, 243, 289, 324, 343]); for(q=1, #l, if(n==l[q], return(0))); k=1; while(k, s=(n^prime(k)-1)/(n-1); if(ispseudoprime(s), return(prime(k))); k++)}
n=2; while(n<361, print1(a(n), ", "); n++) \\ Derek Orr, Jul 13 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003
EXTENSIONS
More terms from T. D. Noe, Jan 23 2004
STATUS
approved