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A003020
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Largest prime factor of the "repunit" number 11...1 (cf. A002275)
(Formerly M4790)
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15
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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
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OFFSET
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2,1
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REFERENCES
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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.
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LINKS
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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
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FORMULA
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a(n) = A006530(A002275(n)). - Ray Chandler, Apr 22 2017
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n)=local(p); if(n<2, n==1, p=factor((10^n-1)/9)~[1, ]; p[length(p)])
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CROSSREFS
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Cf. A002275, 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
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Harvey P. Dale, Jan 17 2001
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STATUS
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approved
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