

A004062


Numbers n such that (6^n  1)/5 is prime.
(Formerly M0861)


24



2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099
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OFFSET

1,1


COMMENTS

Prime repunits in base 6.
With this 15th 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), 927930.
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^n1)/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



