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
P. Bourdelais, A Generalized Repunit Conjecture
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
H. Lifchitz, Mersenne and Fermat primes field
MATHEMATICA
lst={}; Do[If[PrimeQ[(13^n-1)/12], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)
PROG
(PARI) is(n)=isprime((13^n-1)/12) \\ Charles R Greathouse IV, Feb 17 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
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