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A016054
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Numbers n such that (13^n - 1)/12 is prime.
(Formerly M2708)
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16
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5, 7, 137, 283, 883, 991, 1021, 1193, 3671, 18743, 31751, 101089
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| For Repunits in bases from -14 to 14, base 13 is a lucky number with the highest relative rate of primes being discovered. Base 7 is the most unlucky base with the lowest rate of primes being discovered. There is a Generalized Repunit Conjecture implying that all bases will eventually converge to the same relative rate of occurrence (ref 1). [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 01 2010]
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REFERENCES
| H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Paul Bourdelais, Title?
H. Lifchitz, Mersenne and Fermat primes field
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MATHEMATICA
| lst={}; Do[If[PrimeQ[(13^n-1)/12], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 21 2008]
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PROG
| (Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 01 2010]
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CROSSREFS
| Sequence in context: A176619 A088270 A065927 * A158969 A083842 A164372
Adjacent sequences: A016051 A016052 A016053 * A016055 A016056 A016057
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Error in first term corrected Aug 15 1997 by Robert G. Wilson v (rgwv(AT)rgwv.com).
18743 (probable prime) from David Radcliffe (dradcliffe(AT)gmail.com), Jul 04 2004
One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
a(12)=101089 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Mar 01 2010
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