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

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

Offset

1,2

Comments

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).

Links

Jianing Song, Rows n = 1..32, flattened

Example

The table T(k,m), m = 1..A059892(k), begins
  1, 3, 9;
  11, 33, 99;
  27, 37, 111, 333, 999;
  etc.

Maple

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;

Prog

(PARI) Row(n) = my(v=divisors(10^n-1)); select(x->(znorder(Mod(10, x))==n), v) \\ Jianing Song, Jun 15 2021

Crossrefs

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.

Sequence in context: A175203 A018282 A057245 * A027894 A249647 A004668

Adjacent sequences: A226474 A226475 A226476 * A226478 A226479 A226480

Keyword

nonn,base,tabf,easy

Author

Martin Renner, Jun 08 2013

Status

approved