A016054 Numbers n such that (13^n - 1)/12 is prime. (Formerly M2708)

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

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), 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

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