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A004063 Numbers n such that (7^n - 1)/6 is prime.
(Formerly M3836)
+0
15
5, 13, 131, 149, 1699, 14221, 35201, 126037 (list; graph; listen)
OFFSET

1,1

COMMENT

Base 7 repunit primes. - Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Aug 31 2007

a(7)=35201 is a probable prime with trial factoring to 7e12 and Fermat base 2 primality test. - Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Aug 31 2007

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

LINKS

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, Link to a section of The World of Mathematics.

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

CROSSREFS

Sequence in context: A106046 A117527 A155175 this_sequence A005764 A099974 A159261

Adjacent sequences: A004060 A004061 A004062 this_sequence A004064 A004065 A004066

KEYWORD

nonn,hard

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

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

a(7) from Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), 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 2.5e13 and Fermat base 2 primality test. Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Sep 18 2008

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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