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 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 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), 927-930. H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [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)^n-1)/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 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

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)