A005422 Largest prime factor of 10^n - 1.

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

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.
• 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

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.

Programs

Magma

[Maximum(PrimeDivisors(10^n-1)): n in [1..45]]; // Vincenzo Librandi, Jul 13 2016

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 *)

PARI

a(n)=vecmax(factor(10^n-1)[,1]) \\ Simplified by M. F. Hasler, Jul 30 2015

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

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