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A309589
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Number subsets {0, ..., 10^k - 1} written in base 10 and sorted lexicographically, for k = 1, 2, ...
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2
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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Georg Fischer, Perl program which generates this sequence and its inverse.
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EXAMPLE
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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: ...
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PROG
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(Perl) # cf. link
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CROSSREFS
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Cf. A119589 (like row k=2, but 1 <= i <= 100), A190016 (like row k=4, but 1 <= i <= 10000), A309590 (inverse)
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KEYWORD
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nonn,base,easy,tabf
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AUTHOR
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STATUS
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approved
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