A003020 Largest prime factor of the "repunit" number 11...1 (cf. A002275).

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: 2

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

a(n) = R_n iff n is a term of A004023. - Bernard Schott, Jul 07 2022

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, Introduction à la Théorie des Nombres. Gauthier-Villars, Paris, 1952, p. 40.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• David Wells, The Factors of the Repunits 11 through R_40, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, 1986, p. 219.

Links

• Max Alekseyev, Table of n, a(n) for n = 2..352 (terms a(2)..a(100) from T. D. Noe, derived from data from Yousuke Koide; a(101)..a(322) from Ray Chandler)
• J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
• Patrick De Geest, Repunits and their Prime Factors
• Makoto Kamada, Factorizations of 11...11 (Repunit).
• Yousuke Koide, Factorizations of Repunit Numbers
• A. A. D. Steward, Factorization of Repunits[up to R(196)] [Broken link]
• S. S. Wagstaff, Jr., The Cunningham Project

Crossrefs

Cf. A002275, A004023, A006530, A102380.

Same as A005422 except for initial terms.

Smallest factor: A067063.

Programs

Mathematica

Table[Max[Transpose[FactorInteger[10^i - 1]][[1]]], {i, 2, 25}]
Table[FactorInteger[FromDigits[PadRight[{},n,1]]][[-1,1]],{n,2,30}] (* Harvey P. Dale, Feb 01 2014 *)

PARI

a(n)=local(p); if(n<2,n==1,p=factor((10^n-1)/9)~[1,]; p[length(p)])

Formula

a(n) = A006530(A002275(n)). - Ray Chandler, Apr 22 2017

Extensions

More terms from Harvey P. Dale, Jan 17 2001