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Search: id:A003020
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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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+0
11
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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
(list; graph; listen)
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OFFSET
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2,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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 \`{a} la Th\'{e}orie des Nombres. Gauthier-Villars, Paris, 1952, p. 40.
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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T. D. Noe, Table of n, a(n) for n=2..100 (derived from Yousuke Koide)
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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MATHEMATICA
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Table[Max[Transpose[FactorInteger[10^i - 1]][[1]]], {i, 2, 25}]
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PROGRAM
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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, A102380. Same as A005422 except for initial terms. Smallest factor: A067063.
Sequence in context: A090950 A124479 A140373 this_sequence A075024 A152094 A147556
Adjacent sequences: A003017 A003018 A003019 this_sequence 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 (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Harvey P. Dale (hpd1(AT)nyu.edu), Jan 17 2001
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