

A004062


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


15



2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, 1365019
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Prime repunits in base 6.
With this 16th prime, the base 6 repunits have an average (best linear fit) occurrence rate of G = 0.4948 which seems to be converging to the conjectured rate of 0.56146 (see ref).


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.
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..16.
John Brillhart et al., Cunningham Project [Factorizations of b^n + 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers]
Paul Bourdelais, A Generalized Repunit Conjecture.  Paul Bourdelais, May 24 2010
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927930.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927930. [Annotated scanned copy]
H. Lifchitz, Mersenne and Fermat primes field
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
Index to primes in various ranges, form ((k+1)^n1)/k


MATHEMATICA

Select[Range[1000], PrimeQ[(6^#  1)/5] &] (* Alonso del Arte, Dec 31 2019 *)


PROG

(PARI) is(n)=isprime((6^n  1)/5) \\ Charles R Greathouse IV, Apr 28 2015


CROSSREFS

Sequence in context: A061092 A084435 A072469 * A037151 A326358 A008840
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) discovered Nov 05 2007, corresponds to a probable prime based on trial factoring to 10^11 and Fermat primality test base 2.  Paul Bourdelais
a(15) corresponds to a probable prime discovered by Paul Bourdelais, May 24 2010
a(16) corresponds to a probable prime discovered by Paul Bourdelais, Dec 31 2019


STATUS

approved



