|
| |
|
|
A004062
|
|
Numbers n such that (6^n - 1)/5 is prime.
(Formerly M0861)
|
|
22
|
|
|
|
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 15th prime, the base 6 repunits have an average (best linear fit) occurrence rate of G=.48453 which seems to be converging to the conjectured rate of .56146 (see ref). [From 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 [From Vladimir Joseph Stephan Orlovsky, Aug 21 2008]
|
|
|
PROG
|
(Other) PFGW v3.3.1 [From 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 1E11 and Fermat primality test base 2. - Paul Bourdelais (paul.bourdelais(AT)gd-ais.com).
a(15)=608099 is a probable prime discovered by Paul Bourdelais, May 24 2010
|
|
|
STATUS
|
approved
|
| |
|
|
