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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

Programs

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 *)

PARI

is(n)=isprime((13^n-1)/12) \\ Charles R Greathouse IV, Feb 17 2017

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