A006035 Numbers n such that (19^n-1)/18 is prime.

19, 31, 47, 59, 61, 107, 337, 1061, 9511, 22051, 209359

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

No others less than 8011. - Julien Peter Benney (jpbenney(AT)ftml.net), Aug 15 2004

a(9) = 9511 was found by Richard Fischer on Dec 15 2004. - Alexander Adamchuk, Feb 11 2007

References

• Ribenboim, Paulo; "The Book Of Prime Number Records"; published 1989 by Springer-Verlag; pages 350-354.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Paul Bourdelais, A Generalized Repunit Conjecture. - _Paul Bourdelais_, Aug 27 2010
• 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
• Index to primes in various ranges, form ((k+1)^n-1)/k

Programs

Mathematica

lst={};Do[If[PrimeQ[(19^n-1)/18], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

PARI

is(n)=isprime((19^n-1)/18) \\ Charles R Greathouse IV, Apr 28 2015

Extensions

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

a(11)=209359 corresponds to a probable prime discovered by Paul Bourdelais, Aug 27 2010