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A004063 Numbers n such that (7^n - 1)/6 is prime.
(Formerly M3836)
34
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

For Repunits with bases from -11 to 11, base 7 Repunits have the lowest relative rate of occurrence 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.

H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.

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..10.

Paul Bourdelais,A Generalized Repunit Conjecture

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

H. Lifchitz, Mersenne and Fermat primes field

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"

CROSSREFS

Sequence in context: A228280 A155175 A213129 * A005764 A099974 A247820

Adjacent sequences:  A004060 A004061 A004062 * A004064 A004065 A004066

KEYWORD

nonn,hard

AUTHOR

N. J. A. Sloane.

EXTENSIONS

a(6) from Robert G. Wilson v, Apr 09 2005

a(7)=35201 is a probable prime from Paul Bourdelais, Aug 31 2007

a(8)=126037 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)=371669 is a probable prime discovered by Paul Bourdelais, Feb 23 2010

a(10)=1264699 is a probable prime discovered by Paul Bourdelais, Jan 06 2014

STATUS

approved

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Last modified December 19 12:55 EST 2014. Contains 252225 sequences.