cp's OEIS Frontend

A016054 Numbers n such that (13^n - 1)/12 is prime.

%I A016054 M2708 #45 Apr 11 2020 06:27:15
%S A016054 5,7,137,283,883,991,1021,1193,3671,18743,31751,101089,1503503
%N A016054 Numbers n such that (13^n - 1)/12 is prime.
%C A016054 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
%D A016054 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A016054 P. Bourdelais, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;417ab0d6.0906">A Generalized Repunit Conjecture</a>
%H A016054 H. Dubner, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1185243-9">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930.
%H A016054 H. Dubner, <a href="/A028491/a028491.pdf">Generalized repunit primes</a>, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
%H A016054 H. Lifchitz, <a href="http://www.primenumbers.net/Henri/us/MersFermus.htm">Mersenne and Fermat primes field</a>
%t A016054 lst={};Do[If[PrimeQ[(13^n-1)/12], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* _Vladimir Joseph Stephan Orlovsky_, Aug 21 2008 *)
%o A016054 (PARI) is(n)=isprime((13^n-1)/12) \\ _Charles R Greathouse IV_, Feb 17 2017
%K A016054 nonn
%O A016054 1,1
%A A016054 _N. J. A. Sloane_
%E A016054 Error in first term corrected by _Robert G. Wilson v_, Aug 15 1997
%E A016054 a(10) (corresponds to a probable prime) from _David Radcliffe_, Jul 04 2004
%E A016054 a(11) from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
%E A016054 a(12) corresponds to a probable prime discovered by _Paul Bourdelais_, Mar 01 2010
%E A016054 a(13) corresponds to a probable prime discovered by _Paul Bourdelais_, Apr 09 2020