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A003060
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Smallest number with reciprocal of period length n in decimal (base 10).
(Formerly M2886)
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9
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1, 3, 11, 27, 101, 41, 7, 239, 73, 81, 451, 21649, 707, 53, 2629, 31, 17, 2071723, 19, 1111111111111111111, 3541, 43, 23, 11111111111111111111111, 511, 21401, 583, 243, 29, 3191, 211, 2791, 353, 67, 103, 71, 1919, 2028119, 909090909090909091
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OFFSET
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0,2
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COMMENTS
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For n > 0, a(n) is the least divisor d > 1 of 10^n - 1 such that the multiplicative order of 10 mod d is n. For prime n > 3, a(n) = A007138(n). - T. D. Noe, Aug 07 2007
For n > 1, a(n) is the smallest positive d such that d divides 10^n - 1 and does not divide any of 10^k - 1 for 0 < k < n. - Maciej Ireneusz Wilczynski, Sep 06 2012, corrected by M. F. Hasler, Jun 28 2022. (For n = 1, d = 1 divides 10^n - 1 and does not divide any 10^k - 1 with 0 < k < n, but a(1) = 3 > 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.
"Cycle lengths of reciprocals", Popular Computing (Calabasas, CA), Vol. 1 (No. 4, Jul 1973), pp. 12-14.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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MATHEMATICA
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a[n_] := First[ Select[ Divisors[10^n - 1], MultiplicativeOrder[10, #] == n &, 1]]; a[0] = 1; a[1] = 3; Table[a[n], {n, 0, 38}] (* Jean-François Alcover, Jul 13 2012, after T. D. Noe *)
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PROG
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(PARI) apply( {A003060(n)=!fordiv(10^n-!!n, d, d>1 && znorder(Mod(10, d))==n && return(d))}, [0..50]) \\ M. F. Hasler, Jun 28 2022
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CROSSREFS
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Smallest primitive divisors of b^n-1: A212953 (b=2), A218356 (b=3), A218357 (b=5), A218358 (b=7), this sequence (b=10), A218359 (b=11), A218360 (b=13), A218361 (b=17), A218362 (b=19), A218363 (b=23), A218364 (b=29).
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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b-file truncated at uncertain term a(439) by Max Alekseyev, Apr 30 2022
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STATUS
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approved
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