A004062 Numbers k such that (6^k - 1)/5 is prime. (Formerly M0861)

2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, 1365019, 3360347

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).

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.

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..17.

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

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

a(17) corresponds to a probable prime discovered by Ryan Propper, Oct 30 2023

Status

approved