

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^n1 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. 1214.
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}] (* JeanFrançois 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



