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A004063
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Numbers k such that (7^k - 1)/6 is prime.
(Formerly M3836)
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21
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OFFSET
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1,1
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COMMENTS
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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
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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.
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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J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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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(Prime95) PRP=1, 7, 1264699, -1, 0, 0, "6"
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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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
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STATUS
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approved
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