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A084740
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Least k such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists.
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15
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2, 3, 2, 3, 2, 5, 3, 0, 2, 17, 2, 5, 3, 3, 2, 3, 2, 19, 3, 3, 2, 5, 3, 0, 7, 3, 2, 5, 2, 7, 0, 3, 13, 313, 2, 13, 3, 349, 2, 3, 2, 5, 5, 19, 2, 127, 19, 0, 3, 4229, 2, 11, 3, 17, 7, 3, 2, 3, 2, 7, 3, 5, 0, 19, 2, 19, 5, 3, 2, 3, 2, 5, 5, 3, 41, 3, 2, 5, 3, 0, 2, 5, 17, 5, 11, 7, 2, 3, 3, 4421, 439, 7, 5, 7, 2, 17, 13, 3, 2, 3, 2, 19, 97, 3, 2, 17, 2, 17, 3, 3, 2, 23, 29, 7, 59
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OFFSET
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2,1
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COMMENTS
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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
More terms: a(135) = 1171, a(142) = 1231, a(174) = 3251, a(230) = 5333, a(244) = 3331, a(259) = 2011, a(284) = 2473, a(318) = 1193, a(333) = 9743, a(360) = 2609; for n up to 360, a(n) is currently unknown only for n = {152, 184, 185, 200, 269, 281, 311, 326, 331}. All other terms up to a(360) are less than 1000. - Eric Chen, Nov 14 2014
a(n) corresponds only to probable primes for n = {51, 91, 174, 230, 244, 259, 284, 333, 360}. - Eric Chen, Nov 14 2014
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
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LINKS
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Table of n, a(n) for n=2..116.
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.
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A065507, A065854, A084738, A084742, A096059, A126659, A128164, A246005.
Cf. A066180, A085398, A103795, A123487, A123627.
Sequence in context: A256113 A256368 A057019 * A229708 A204895 A064652
Adjacent sequences: A084737 A084738 A084739 * A084741 A084742 A084743
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003
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EXTENSIONS
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More terms from T. D. Noe, Jan 23 2004
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STATUS
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approved
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