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%I M2886 #39 Jul 03 2022 09:16:55
%S 1,3,11,27,101,41,7,239,73,81,451,21649,707,53,2629,31,17,2071723,19,
%T 1111111111111111111,3541,43,23,11111111111111111111111,511,21401,583,
%U 243,29,3191,211,2791,353,67,103,71,1919,2028119,909090909090909091
%N Smallest number with reciprocal of period length n in decimal (base 10).
%C 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
%C 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.)
%D J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.
%D "Cycle lengths of reciprocals", Popular Computing (Calabasas, CA), Vol. 1 (No. 4, Jul 1973), pp. 12-14.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A003060/b003060.txt">Table of n, a(n) for n = 0..438</a>
%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%t 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_ *)
%o (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
%Y 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).
%Y Cf. A007138, A057951, A005422, A176973.
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_
%E Comment corrected by _T. D. Noe_, Apr 15 2010
%E More terms from _T. D. Noe_, Apr 15 2010
%E b-file truncated at uncertain term a(439) by _Max Alekseyev_, Apr 30 2022
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