A002591 Largest prime factor of 3^(2n+1) - 1. (Formerly M4886 N2095)

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

0,1

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

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A213306 A213307 A213305 * A037055 A065584 A153651

Adjacent sequences: A002588 A002589 A002590 * A002592 A002593 A002594

Keyword

nonn

Author

N. J. A. Sloane

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

Status

approved