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A003060 Smallest number with reciprocal of period n.
(Formerly M2886)
4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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 nonnegative n, 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

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.

"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).

LINKS

T. D. Noe, Table of n, a(n) for n=0..500

Index entries for sequences related to decimal expansion of 1/n

MATHEMATICA

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-Fran├žois Alcover, Jul 13 2012, after T. D. Noe *)

CROSSREFS

Sequence in context: A077776 A113836 A036571 * A136983 A210611 A119074

Adjacent sequences:  A003057 A003058 A003059 * A003061 A003062 A003063

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Comment corrected by T. D. Noe, Apr 15 2010

More terms from T. D. Noe, Apr 15 2010

STATUS

approved

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Last modified December 10 20:55 EST 2018. Contains 318049 sequences. (Running on oeis4.)