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A226477 Table (read by rows) of the natural numbers (in ascending order) whose reciprocals have only periodic decimals of length k.

%I A226477 #15 Jun 15 2021 02:02:20
%S A226477 1,3,9,11,33,99,27,37,111,333,999,101,303,909,1111,3333,9999,41,123,
%T A226477 271,369,813,2439,11111,33333,99999,7,13,21,39,63,77,91,117,143,189,
%U A226477 231,259,273,297,351,407,429,481,693,777,819,1001,1221,1287,1443,2079,2331,2457,2849,3003,3367,3663,3861,4329,5291,6993,8547,9009,10101,10989,12987,15873,25641,27027,30303,37037,47619,76923,90909,111111,142857,333333,999999
%N A226477 Table (read by rows) of the natural numbers (in ascending order) whose reciprocals have only periodic decimals of length k.
%C A226477 The k-th row always ends with 10^k - 1 = 99..99 (k times 9).
%C A226477 The number of elements in row k is A059892(k).
%H A226477 Jianing Song, <a href="/A226477/b226477.txt">Rows n = 1..32, flattened</a>
%e A226477 The table T(k,m), m = 1..A059892(k), begins
%e A226477   1, 3, 9;
%e A226477   11, 33, 99;
%e A226477   27, 37, 111, 333, 999;
%e A226477   etc.
%p A226477 a:=[1,3,9]: S:={1,3,9}: for k from 2 to 6 do T:=numtheory[divisors](10^k-1): a:=[op(a),op(T minus S)]: S:=S union T; od: a;
%o A226477 (PARI) Row(n) = my(v=divisors(10^n-1)); select(x->(znorder(Mod(10,x))==n), v) \\ _Jianing Song_, Jun 15 2021
%Y A226477 Cf. A018282, A018766, A027894, A027893, A027892, A027891, A027890, A027889, A027895, A027896, A027897, A109933, A106305, A111117, A111211, A113116, A113522 (Divisors of 10^k - 1, k = 2..18), A059892, A084680.
%K A226477 nonn,base,tabf,easy
%O A226477 1,2
%A A226477 _Martin Renner_, Jun 08 2013