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A004063
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Numbers n such that (7^n - 1)/6 is prime.
(Formerly M3836)
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25
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OFFSET
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1,1
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COMMENTS
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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
For Repunits with bases from -11 to 11, base 7 Repunits have the lowest relative rate of occurrence so far. [From Paul Bourdelais, Feb 23 2010]
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=1..9.
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.
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MATHEMATICA
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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
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PROG
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(Other) PFGW v3.3.1 [From Paul Bourdelais, Feb 23 2010]
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CROSSREFS
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Sequence in context: A117527 A155175 A213129 * A005764 A099974 A187894
Adjacent sequences: A004060 A004061 A004062 * A004064 A004065 A004066
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KEYWORD
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nonn,hard
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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a(6) from Robert G. Wilson v, 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
a(9)=371669 is a probable prime discovered by Paul Bourdelais, Feb 23 2010
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STATUS
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approved
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