A309589 Number subsets {0, ..., 10^k - 1} written in base 10 and sorted lexicographically, for k = 1, 2, ...

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 60, 61

Offset: 0

Author

Georg Fischer, Mar 02 2019

Keywords

• nonn
• base
• easy
• tabf

Comments

The sequence is the flattened form of an irregular table T(k, i). The rows for k >= 1 contain a permutation of the numbers 0 <= i <= 10^k - 1 which is defined by the lexicographical order of the numbers i written in base 10.

This "useless" order appears, for example, in a directory listing of numbered filenames, or after an ASCII sort of signatures of linear recurrences. The Perl program in the link computes this sequence and variations with different ranges and bases.

Examples

			Table T(k, i) begins:
  k\i   0   1   2   3 ...
  -------------------------
  1:    0   1   2   3 ...   9
  2:    0   1  10  11 ...  19   2  20  21 ...  99
  3:    0   1  10 100 ... 109  11 110 111 ... 999
  4:  ...
		

Links

• Georg Fischer, Perl program which generates this sequence and its inverse.

Crossrefs

Cf. A119589 (like row k=2, but 1 <= i <= 100), A190016 (like row k=4, but 1 <= i <= 10000), A309590 (inverse)

Programs

Perl

# cf. link