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A226477
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Table (read by rows) of the natural numbers (in ascending order) whose reciprocals have only periodic decimals of length k.
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2
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1, 3, 9, 11, 33, 99, 27, 37, 111, 333, 999, 101, 303, 909, 1111, 3333, 9999, 41, 123, 271, 369, 813, 2439, 11111, 33333, 99999, 7, 13, 21, 39, 63, 77, 91, 117, 143, 189, 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
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refs;
listen;
history;
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OFFSET
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1,2
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COMMENTS
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The k-th row always ends with 10^k - 1 = 99..99 (k times 9).
The number of elements in row k is A059892(k).
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LINKS
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EXAMPLE
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The table T(k,m), m = 1..A059892(k), begins
1, 3, 9;
11, 33, 99;
27, 37, 111, 333, 999;
etc.
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MAPLE
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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;
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PROG
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(PARI) Row(n) = my(v=divisors(10^n-1)); select(x->(znorder(Mod(10, x))==n), v) \\ Jianing Song, Jun 15 2021
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CROSSREFS
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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.
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KEYWORD
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nonn,base,tabf,easy
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AUTHOR
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STATUS
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approved
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