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 A028491 Numbers n such that (3^n - 1)/2 is prime. (Formerly M2643) 70
 3, 7, 13, 71, 103, 541, 1091, 1367, 1627, 4177, 9011, 9551, 36913, 43063, 49681, 57917, 483611, 877843, 2215303 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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, Feb 09 2005 Salas lists these, except 3, in "Open Problems" p.6 [March 2012], and proves that the Cantor primes > 3 are exactly the prime-valued cyclotomic polynomials of the form Phi_s(3^{s^j}) == 1 (mod 4). Also, n such that 3^n-1 is a semiprime - see also A080892. - M. F. Hasler, Mar 19 2013 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). LINKS Antal Bege, Kinga Fogarasi, Generalized perfect numbers, arXiv:1008.0155 [math.NT], 2010. See p. 81. Paul Bourdelais, A Generalized Repunit Conjecture, Posting in NMBRTHRY@LISTSERV.NODAK.EDU, Jun 25, 2009. 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. H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930. [Annotated scanned copy] H. Lifchitz, Mersenne and Fermat primes field Christian Salas, Cantor Primes as Prime-Valued Cyclotomic Polynomials, arXiv:1203.3969v1 [math.NT], Mar 18, 2012. 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 MATHEMATICA Do[If[PrimeQ[(3^n-1)/2], Print[n]], {n, 10000}] (* Farideh Firoozbakht, Feb 09 2005 *) PROG (PARI) forprime(p=2, 1e5, if(ispseudoprime(3^p\2), print1(p", "))) \\ Charles R Greathouse IV, Jul 15 2011 CROSSREFS Cf. A076481, A033632. Sequence in context: A228209 A176903 A004060 * A137474 A071087 A038691 Adjacent sequences:  A028488 A028489 A028490 * A028492 A028493 A028494 KEYWORD nonn,more,hard AUTHOR N. J. A. Sloane, Jean-Yves Perrier (nperrj(AT)ascom.ch) EXTENSIONS a(13) from Farideh Firoozbakht, Mar 27 2005 a(14)-a(16) from Robert G. Wilson v, Apr 11 2005 a(17) corresponds to a probable prime discovered by Paul Bourdelais, Feb 08 2010 a(18) corresponds to a probable prime discovered by Paul Bourdelais, Jul 06 2010 a(19) corresponds to a probable prime discovered by Paul Bourdelais, Feb 05 2019 STATUS approved

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Last modified May 26 13:49 EDT 2020. Contains 334626 sequences. (Running on oeis4.)