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A003020 Largest prime factor of the "repunit" number 11...1 (cf. A002275)
(Formerly M4790)
14
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

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, 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, p. 219 Penguin 1986.

LINKS

Ray Chandler, Table of n, a(n) for n = 2..322 (first 99 terms from T. D. Noe)

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

P. 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, A006530, A102380. Same as A005422 except for initial terms. Smallest factor: A067063.

Sequence in context: A217947 A124479 A140373 * A075024 A229612 A210321

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

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.