

A004062


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


17



2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, 1365019, 3360347
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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^k1 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

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 *)


PROG



CROSSREFS



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


STATUS

approved



