

A016054


Numbers n such that (13^n  1)/12 is prime.
(Formerly M2708)


14



5, 7, 137, 283, 883, 991, 1021, 1193, 3671, 18743, 31751, 101089, 1503503
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OFFSET

1,1


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).  Paul Bourdelais, Mar 01 2010


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..13.
P. Bourdelais, A Generalized Repunit Conjecture
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927930.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927930. [Annotated scanned copy]
H. Lifchitz, Mersenne and Fermat primes field


MATHEMATICA

lst={}; Do[If[PrimeQ[(13^n1)/12], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)


PROG

(PARI) is(n)=isprime((13^n1)/12) \\ Charles R Greathouse IV, Feb 17 2017


CROSSREFS

Sequence in context: A224507 A065927 A217726 * A158969 A083842 A164372
Adjacent sequences: A016051 A016052 A016053 * A016055 A016056 A016057


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Error in first term corrected by Robert G. Wilson v, Aug 15 1997
a(10) (corresponds to a probable prime) from David Radcliffe, Jul 04 2004
a(11) from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
a(12) corresponds to a probable prime discovered by Paul Bourdelais, Mar 01 2010
a(13) corresponds to a probable prime discovered by Paul Bourdelais, Apr 09 2020


STATUS

approved



