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A004061
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Numbers n such that (5^n - 1)/4 is prime.
(Formerly M2620)
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40
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3, 7, 11, 13, 47, 127, 149, 181, 619, 929, 3407, 10949, 13241, 13873, 16519, 201359, 396413
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| With the addition of the 17th prime in the sequence, the new best linear fit to the sequence has G=.44676 which is slightly closer to the conjectured limit of G=0.56145948 (see link for Generalized Repunit Conjecture). [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jun 01 2010]
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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).
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LINKS
| Paul Bourdelais,A Generalized Repunit Conjecture [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jun 01 2010]
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
| lst={}; Do[If[PrimeQ[(5^n-1)/4], AppendTo[lst, n]], {n, 10^4}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 20 2008]
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PROG
| (Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jun 01 2010]
(PARI) forprime(p=2, 1e4, if(ispseudoprime(5^p\4), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Sequence in context: A053728 A059055 A145670 * A000572 A059568 A003512
Adjacent sequences: A004058 A004059 A004060 * A004062 A004063 A004064
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KEYWORD
| hard,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| 3 more terms from Kamil Duszenko (kdusz(AT)wp.pl), Mar 25 2003
a(16)=201359 is a probable prime based on trial factoring to 4e13 and Fermat primality testing base 2. Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Dec 11 2008
a(17)=396413 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jun 01 2010
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