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 A002587 Largest prime factor of 2^n + 1. (Formerly M2386 N0948) 17
 2, 3, 5, 3, 17, 11, 13, 43, 257, 19, 41, 683, 241, 2731, 113, 331, 65537, 43691, 109, 174763, 61681, 5419, 2113, 2796203, 673, 4051, 1613, 87211, 15790321, 3033169, 1321, 715827883, 6700417, 20857, 26317, 86171, 38737, 25781083, 525313 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n) != 1 (mod n) for n = 3, 51, 141, 309, 321, 348, ... - Giovanni Resta & Thomas Ordowski, Jan 05 2014 a(n) != 1 (mod n) iff a(m) = a(n) for some m < n. Then n = 3m for m = 1, 17, 47, 103, 107, 116, ... - Thomas Ordowski, Jan 08 2014 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. M. Kraitchik, Recherches sur la Théorie des Nombres. Gauthiers-Villars, Paris, Vol. 1, 1924, Vol. 2, 1929, see Vol. 2, p. 85. E. Lucas, Théorie des fonctions numériques simplement périodiques, Amer. J. Math., 1 (1878), 184-239, 289-321. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002. D. X. Charles, The abc-conjecture and the largest prime factor of 2^n + 1 E. Lucas, Théorie des Fonctions Numériques Simplement Périodiques, I", Amer. J. Math., 1 (1878), 184-240, 289-321. See pages 239 and 240. Edouard Lucas, The Theory of Simply Periodic Numerical Functions, Fibonacci Association, 1969. English translation of article "Théorie des Fonctions Numériques Simplement Périodiques, I", Amer. J. Math., 1 (1878), 184-240. S. S. Wagstaff, Jr., The Cunningham Project FORMULA Charles proves that a(n) >> n^(4/3) infinitely often under the abc conjecture, and reports that Andrew Granville has improved this to a(n) >> n^2. - Charles R Greathouse IV, Apr 29 2013 a(n) = A006530(A000051(n)). - Vincenzo Librandi, Jul 12 2016 MATHEMATICA Table[FactorInteger[2^n + 1][[-1, 1]], {n, 0, 30}] (* Vincenzo Librandi, Jul 12 2016 *) PROG (MAGMA) [Maximum(PrimeDivisors(2^n+1)): n in [0..40]]; // Vincenzo Librandi, Jul 12 2016 (PARI) a(n)=my(f=factor(2^n+1)[, 1]); f[#f] \\ Charles R Greathouse IV, Jul 12 2016 CROSSREFS Cf. A000051, A002586, A006530. Cf. similar sequences listed in A274903. Sequence in context: A209195 A113222 A060444 * A152814 A280319 A021981 Adjacent sequences:  A002584 A002585 A002586 * A002588 A002589 A002590 KEYWORD nonn AUTHOR EXTENSIONS More terms from James A. Sellers, Jul 06 2000 Terms up to a(500) in b-file from T. D. Noe, Nov 10 2007 Offset 0, a(0) = 2 from Vincenzo Librandi, Jul 12 2016 Terms a(1037)-a(1062) in b-file from Amiram Eldar, Feb 01 2020 Terms a(501)-a(1036), a(1063)-a(1075) in b-file from Max Alekseyev, Apr 23 2019, Sep 10 2020 STATUS approved

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Last modified November 27 18:22 EST 2020. Contains 338683 sequences. (Running on oeis4.)