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A007658
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Numbers n such that (3^n + 1)/4 is prime.
(Formerly M2420)
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13
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3, 5, 7, 13, 23, 43, 281, 359, 487, 577, 1579, 1663, 1741, 3191, 9209, 11257, 12743, 13093, 17027, 26633, 104243, 134227, 152287, 700897
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Prime repunits in base -3.
a(22)=134227, discovered Nov 08 2007, is a probable prime based on trial factoring to 1E12 and Fermat primality test base 2. - Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Nov 09 2007
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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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
H. Lifchitz, Mersenne and Fermat primes field
Paul Bourdelais,A Generalized Repunit Conjecture [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Apr 05 2010]
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MATHEMATICA
| lst={}; Do[If[PrimeQ[(3^n+1)/4], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 21 2008]
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PROG
| (Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Apr 05 2010]
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CROSSREFS
| Sequence in context: A077949 A077974 A126273 * A154321 A024724 A024946
Adjacent sequences: A007655 A007656 A007657 * A007659 A007660 A007661
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KEYWORD
| hard,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| a(20) from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 11 2005
a(23)=152287 is a probable prime based on Fermat primality testing and trial factoring to 3E13. - Paul Bourdelais (paul.bourdelais(AT)gd-ais.com), Apr 07 2008
a(24)=700897 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Apr 05 2010
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