A002591 Largest prime factor of 3^(2n+1) - 1.

2, 13, 11, 1093, 757, 3851, 797161, 4561, 34511, 363889, 368089, 1001523179, 391151, 8209, 20381027, 4404047, 2413941289, 2664097031, 17189128703, 797161, 86950696619, 380808546861411923, 927001, 96656723, 131713, 99810171997

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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. 28.
• 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

• Table of n, a(n) for n = 0..344
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Together with A274909 forms bisection of A074477.Cf. A057958, A059885, A085028, A133801, A235366.

Programs

Mathematica

Table[FactorInteger[3^(2n-1)-1][[-1,1]],{n,30}] (* Harvey P. Dale, Oct 19 2022 *)

Formula

a(n) = A074477(2n+1). - Max Alekseyev, May 22 2022

Extensions

Corrected and extended by Jud McCranie, Jan 03 2001

Terms up to a(307) in b-file from Sean A. Irvine, Apr 20 2014

a(0) prepended and a(308)-a(344) added to b-file by Max Alekseyev, Apr 24 2019, Sep 10 2020, Aug 26 2021, May 22 2022