A004062 - OEIS
2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, 1365019, 3360347
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).
Also, numbers k such that 6^k-1 is semiprime. - Sean A. Irvine, Oct 16 2023
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.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 236.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
John Brillhart et al., Cunningham Project [Factorizations of b^n +- 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers]
Eric Weisstein's World of Mathematics, Repunit
MATHEMATICA
Select[Range[1000], PrimeQ[(6^# - 1)/5] &] (* Alonso del Arte, Dec 31 2019 *)
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
a(17) corresponds to a probable prime discovered by Ryan Propper, Oct 30 2023