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A004063 Numbers k such that (7^k - 1)/6 is prime.
(Formerly M3836)
21
5, 13, 131, 149, 1699, 14221, 35201, 126037, 371669, 1264699 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Base-7 repunit primes. - Paul Bourdelais, Aug 31 2007
Among repunits with bases from -11 to 11, base-7 repunits have the lowest relative rate of occurrence of primes so far. - Paul Bourdelais, Feb 23 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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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]
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
MATHEMATICA
For[n = 1, n <= 20000, n++, If[PrimeQ[(7^n - 1)/6 ], Print[n]]] (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Aug 09 2006 *)
PROG
(Prime95) PRP=1, 7, 1264699, -1, 0, 0, "6"
(PARI) is(n)=isprime((7^n - 1)/6) \\ Charles R Greathouse IV, Apr 28 2015
CROSSREFS
Sequence in context: A155175 A155185 A213129 * A005764 A358922 A305643
KEYWORD
nonn,hard
AUTHOR
EXTENSIONS
a(6) from Robert G. Wilson v, Apr 09 2005
a(7) is a probable prime from Paul Bourdelais, Aug 31 2007
a(8) discovered Sep 17 2008 by Paul Bourdelais & Eric Purohit - it is a probable prime based on trial factoring to 2.5*10^13 and Fermat base 2 primality test. - Paul Bourdelais, Sep 18 2008
a(9) is a probable prime discovered by Paul Bourdelais, Feb 23 2010
a(10) is a probable prime discovered by Paul Bourdelais, Jan 06 2014
STATUS
approved

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Last modified May 19 03:29 EDT 2024. Contains 372666 sequences. (Running on oeis4.)