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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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29
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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, 1205459, 1896463, 2533963
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OFFSET
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1,1
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COMMENTS
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Prime repunits in base -3.
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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..27.
P. Bourdelais,A Generalized Repunit Conjecture
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy]
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
S. S. Wagstaff, Jr., The Cunningham Project
Eric Weisstein's World of Mathematics, Repunit
R. G. Wilson, v, Letter to N. J. A. Sloane, circa 1991.
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MATHEMATICA
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lst={}; Do[If[PrimeQ[(3^n+1)/4], Print[n]; AppendTo[lst, n]], {n, 10^5}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 21 2008 *)
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PROG
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(Other) PFGW v3.3.1 - Paul Bourdelais, Apr 05 2010
(PARI) is(n)=ispseudoprime((3^n+1)/4) \\ Charles R Greathouse IV, Apr 29 2015
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CROSSREFS
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Sequence in context: A077949 A077974 A126273 * A275175 A267549 A154321
Adjacent sequences: A007655 A007656 A007657 * A007659 A007660 A007661
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KEYWORD
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hard,nonn,more
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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EXTENSIONS
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a(20) from Robert G. Wilson v, Apr 11 2005
a(22)=134227 corresponds to a probable prime discovered by Paul Bourdelais, Nov 08 2007
a(23)=152287 corresponds to a probable prime discovered by Paul Bourdelais, Apr 07 2008
a(24)=700897 corresponds to a probable prime discovered by Paul Bourdelais, Apr 05 2010
a(25)=1205459 corresponds to a probable prime discovered by Paul Bourdelais, Aug 28 2015
a(26)=1896463 corresponds to a probable prime discovered by Paul Bourdelais, Jan 30 2020
a(27)=2533963 corresponds to a probable prime discovered by Paul Bourdelais, Mar 06 2020
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STATUS
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approved
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