A006033 Numbers n such that (15^n - 1)/14 is prime. (Formerly M3150)

3, 43, 73, 487, 2579, 8741, 37441, 89009, 505117, 639833

Offset

1,1

Comments

8741 and 37441 are only probable primes. - Julien Peter Benney (jpbenney(AT)ftml.net), Apr 27 2007

References

Paulo Ribenboim, "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..10.

P. Bourdelais, A Generalized Repunit Conjecture

Harvey Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.

H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]

Henri Lifchitz, Mersenne and Fermat primes field

Index to primes in various ranges, form ((k+1)^n-1)/k

Example

(15^3 - 1)/14 = 241, which is prime.

Mathematica

lst={}; Do[If[PrimeQ[(15^n-1)/14], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

Prog

(PARI) is(n)=ispseudoprime((15^n-1)/14) \\ Charles R Greathouse IV, Apr 29 2015

Crossrefs

Cf. A059802, A062647, A003525.

Sequence in context: A139854 A194578 A185632 * A246994 A142184 A199348

Adjacent sequences: A006030 A006031 A006032 * A006034 A006035 A006036

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

a(7) from Julien Peter Benney (jpbenney(AT)ftml.net), Apr 27 2007

a(8) corresponds to a probable prime discovered by Paul Bourdelais, Mar 15 2010

a(9) corresponds to a probable prime discovered by Paul Bourdelais, Jan 14 2015

a(10) corresponds to a probable prime discovered by Paul Bourdelais, Apr 22 2019

Status

approved