A006035 Numbers n such that (19^n-1)/18 is prime. (Formerly M5072)

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

Offset

1,1

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

Table of n, a(n) for n=1..11.

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

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 *)

Prog

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

Crossrefs

Sequence in context: A096787 A104006 A117065 * A104485 A276569 A276447

Adjacent sequences: A006032 A006033 A006034 * A006036 A006037 A006038

Keyword

nonn,more

Author

N. J. A. Sloane

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

Status

approved