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A028491
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Numbers n such that (3^n - 1)/2 is prime.
(Formerly M2643)
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42
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3, 7, 13, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If n is in the sequence and m=3^(n-1) then m is a term of A033632 (phi(sigma(m)) = sigma(phi(m)), so 3^(A028491-1) is a subsequence of A033632. For example since 9551 is in the sequence, phi(sigma(3^9550)) = sigma(phi(3^9550)). - Farideh Firoozbakht (mymontain(AT)yahoo.com), Feb 09 2005
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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
| 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
Paul Bourdelais,A Generalized Repunit Conjecture [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 06 2010]
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MATHEMATICA
| Do[If[PrimeQ[(3^n-1)/2], Print[n]], {n, 10000}] (Firoozbakht)
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PROG
| (Other) PFGW v3.3.1 [From Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 06 2010]
(PARI) forprime(p=2, 1e5, if(ispseudoprime(3^p\2), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A076481, A033632.
Sequence in context: A083201 A176903 A004060 * A137474 A071087 A038691
Adjacent sequences: A028488 A028489 A028490 * A028492 A028493 A028494
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jean-Yves Perrier (nperrj(AT)ascom.ch)
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EXTENSIONS
| 36913 from Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 27 2005
a(14), a(15) & a(16) from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 11 2005
a(17)=483611 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Feb 08 2010
Removed reference to withdrawn paper by Christian Salas. - Charles R Greathouse IV (charles.greathouse(AT)case.edu), Feb 23 2010
a(18)=877843 is a probable prime discovered by Paul Bourdelais (pbourdelais(AT)radiantblue.com), Jul 06 2010
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