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A303171
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Lexicographically earliest sequence of distinct terms such that the successive quantities of digits between two successive 9's are given by the succession of the sequence's digits itself.
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9
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 90, 91, 19, 10, 29, 11, 12, 92, 13, 14, 93, 15, 16, 39, 17, 18, 20, 49, 21, 22, 23, 24, 94, 25, 26, 27, 28, 95, 30, 31, 32, 33, 99, 34, 35, 36, 37, 59, 69, 79, 38, 40, 41, 42, 89, 199, 43, 96, 44, 45, 46, 47, 97, 98, 909, 48, 900, 50, 51, 52, 190, 191, 901, 192, 902
(list;
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listen;
history;
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internal format)
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OFFSET
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1,3
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COMMENTS
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The sequence starts with a(1) = 0 and is always extended with the smallest integer not yet present that doesn't lead to a contradiction.
This sequence is a permutation of the numbers >= 0.
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LINKS
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EXAMPLE
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There are:
0 digit between the 9 of "9" and the 9 of "90";
1 digit between the 9 of "90" and the 9 of "91";
2 digits between the 9 of "91" and the 9 of "19";
3 digits between the 9 of "19" and the 9 of "29";
4 digits between the 9 of "29" and the 9 of "92";
5 digits between the 9 of "92" and the 9 of "93";
6 digits between the 9 of "93" and the 9 of "39";
7 digits between the 9 of "39" and the 9 of "49";
8 digits between the 9 of "49" and the 9 of "94";
9 digits between the 9 of "94" and the 9 of "95";
9 digits between the 9 of "95" and the first 9 of "99";
0 digit between the 9's of "99";
9 digits between the last 9 of "99" and the 9 of "59";
1 digit between the 9 of "59" and the 9 of "69";
etc.
We see that the first column here is the succession of the digits of the sequence, as well as the size of each chunk of digits between two successive 9's.
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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