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A004062
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Numbers n such that (6^n - 1)/5 is prime.
(Formerly M0861)
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15
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2, 3, 7, 29, 71, 127, 271, 509, 1049, 6389, 6883, 10613, 19889, 79987, 608099, 1365019
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OFFSET
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1,1
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COMMENTS
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Prime repunits in base 6.
With this 16th prime, the base 6 repunits have an average (best linear fit) occurrence rate of G = 0.4948 which seems to be converging to the conjectured rate of 0.56146 (see ref).
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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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Table of n, a(n) for n=1..16.
John Brillhart et al., Cunningham Project [Factorizations of b^n +- 1, b = 2, 3, 5, 6, 7, 10, 11, 12 up to high powers]
Paul Bourdelais, A Generalized Repunit Conjecture. - Paul Bourdelais, May 24 2010
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]
H. Lifchitz, Mersenne and Fermat primes field
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
Index to primes in various ranges, form ((k+1)^n-1)/k
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MATHEMATICA
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Select[Range[1000], PrimeQ[(6^# - 1)/5] &] (* Alonso del Arte, Dec 31 2019 *)
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PROG
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(PARI) is(n)=isprime((6^n - 1)/5) \\ Charles R Greathouse IV, Apr 28 2015
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CROSSREFS
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Sequence in context: A061092 A084435 A072469 * A037151 A326358 A008840
Adjacent sequences: A004059 A004060 A004061 * A004063 A004064 A004065
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KEYWORD
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hard,nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Kamil Duszenko (kdusz(AT)wp.pl), Jun 22 2003
a(14) discovered Nov 05 2007, corresponds to a probable prime based on trial factoring to 10^11 and Fermat primality test base 2. - Paul Bourdelais
a(15) corresponds to a probable prime discovered by Paul Bourdelais, May 24 2010
a(16) corresponds to a probable prime discovered by Paul Bourdelais, Dec 31 2019
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STATUS
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approved
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