A005422 Largest prime factor of 10^n - 1. (Formerly M2889)

3, 11, 37, 101, 271, 37, 4649, 137, 333667, 9091, 513239, 9901, 265371653, 909091, 2906161, 5882353, 5363222357, 333667, 1111111111111111111, 27961, 10838689, 513239, 11111111111111111111111, 99990001, 182521213001, 1058313049

Offset

1,1

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.

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 = 1..352

K. Beschorner, Factorizations of Repunit Numbers of the form (10^n-1)/9 (111111...). [Retrieved July 30, 2015]

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

Yousuke Koide, Factorizations of Repunit Numbers.

S. S. Wagstaff, Jr., The Cunningham Project

Formula

For n > 1, a(n) = A003020(n). For 1 < n < 10, a(n) = A075024(n). - M. F. Hasler, Jul 30 2015

a(n) = A006530(A002283(n)). - Vincenzo Librandi, Jul 13 2016

a(A004023(n)) = A002275(A004023(n)). - Bernard Schott, May 24 2022

Maple

A005422 := proc(n)
    10^n-1 ;
    A006530(%) ;
end proc: # R. J. Mathar, Dec 02 2016

Mathematica

Table[FactorInteger[10^n - 1][[-1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Jul 13 2016 *)

Prog

(PARI) a(n)=vecmax(factor(10^n-1)[, 1]) \\ Simplified by M. F. Hasler, Jul 30 2015
(Magma) [Maximum(PrimeDivisors(10^n-1)): n in [1..45]]; // Vincenzo Librandi, Jul 13 2016

Crossrefs

Same as A003020 except for the additional a(1) = 3.

Cf. A002275, A002283, A004023, A006530, A067063, A075024, A102380.

Cf. similar sequences listed in A274906.

Sequence in context: A046107 A243110 A061075 * A040017 A007615 A065540

Adjacent sequences: A005419 A005420 A005421 * A005423 A005424 A005425

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Terms to a(100) in b-file from Yousuke Koide added by T. D. Noe, Dec 06 2006

Edited by M. F. Hasler, Jul 30 2015

a(101)-a(322) in b-file from Ray Chandler, Apr 22 2017

a(323)-a(352) in b-file from Max Alekseyev, Apr 26 2022

Status

approved