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A004062 Numbers n such that (6^n - 1)/5 is prime.
(Formerly M0861)
29
2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Prime repunits in base 6.

With this 15-th prime, the base 6 repunits have an average (best linear fit) occurrence rate of G=0.48453 which seems to be converging to the conjectured rate of 0.56146 (see ref). [Paul Bourdelais, May 24 2010]

REFERENCES

J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

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

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..15.

Paul Bourdelais, A Generalized Repunit Conjecture [From Paul Bourdelais, May 24 2010]

H. Lifchitz, Mersenne and Fermat primes field

S. S. Wagstaff, Jr., The Cunningham Project

Eric Weisstein's World of Mathematics, Repunit.

MATHEMATICA

lst={}; Do[If[PrimeQ[(6^n-1)/5], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)

PROG

(Other) PFGW v3.3.1 [Paul Bourdelais, May 24 2010]

CROSSREFS

Sequence in context: A061092 A084435 A072469 * A037151 A008840 A156313

Adjacent sequences:  A004059 A004060 A004061 * A004063 A004064 A004065

KEYWORD

hard,nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003

a(14)=79987, discovered Nov 05 2007, is a probable prime based on trial factoring to 10^11 and Fermat primality test base 2. - Paul Bourdelais.

a(15)=608099 is a probable prime discovered by Paul Bourdelais, May 24 2010

STATUS

approved

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Last modified December 18 17:15 EST 2014. Contains 252173 sequences.