A003020 Largest prime factor of the "repunit" number 11...1 (cf. A002275). (Formerly M4790)

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

2,1

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

Formula

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

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 *)

Prog

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

Crossrefs

Cf. A002275, A004023, A006530, A102380.

Same as A005422 except for initial terms.

Smallest factor: A067063.

Sequence in context: A124479 A140373 A316191 * A075024 A229612 A297797

Adjacent sequences: A003017 A003018 A003019 * A003021 A003022 A003023

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

More terms from Harvey P. Dale, Jan 17 2001

Status

approved