A002592 Largest prime factor of 9^n + 1.

2, 5, 41, 73, 193, 1181, 6481, 16493, 21523361, 530713, 42521761, 570461, 769, 4795973261, 647753, 47763361, 926510094425921, 1743831169, 282429005041, 25480398173, 128653413121, 109688713, 56625998353, 70601370627701

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. 89.
• 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..345
• 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

Cf. A006530, A062396, A274909.

Cf. similar sequences listed in A274903.

Programs

Magma

[Maximum(PrimeDivisors(9^n+1)): n in [0..40]]; // Vincenzo Librandi, Jul 12 2016

Maple

for n from 0 to 30 do t1:=ifactor(9^n+1); od;

Mathematica

Table[FactorInteger[9^n + 1][[-1, 1]], {n, 0, 10}] (* Vincenzo Librandi, Jul 12 2016 *)

Formula

a(n) = A006530(A062396(n)). - Vincenzo Librandi, Jul 12 2016

a(n) = A074476(2*n). - Max Alekseyev, Apr 25 2022

Extensions

Terms up to a(315) in b-file from Sean A. Irvine, Apr 20 2014

Terms a(316)-a(345) in b-file from Max Alekseyev, Apr 24 2019, Sep 10 2020, Aug 26 2021, Apr 25 2022