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A002592
Largest prime factor of 9^n + 1.
(Formerly M3994 N1655)
10
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
0,1
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. 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
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) = A006530(A062396(n)). - Vincenzo Librandi, Jul 12 2016
a(n) = A074476(2*n). - Max Alekseyev, Apr 25 2022
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 *)
PROG
(Magma) [Maximum(PrimeDivisors(9^n+1)): n in [0..40]]; // Vincenzo Librandi, Jul 12 2016
CROSSREFS
Cf. similar sequences listed in A274903.
Sequence in context: A106885 A072439 A286560 * A054553 A185052 A088547
KEYWORD
nonn
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
STATUS
approved