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A303151
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Lexicographically earliest sequence of distinct terms such that the successive quantities of digits between two successive 1s are given by the succession of the sequence's digits itself.
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11
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0, 1, 10, 12, 11, 2, 13, 3, 14, 15, 16, 4, 17, 18, 5, 6, 19, 7, 8, 101, 9, 20, 21, 31, 22, 23, 41, 51, 24, 25, 26, 100, 27, 121, 28, 29, 30, 61, 71, 32, 33, 34, 35, 102, 36, 81, 37, 38, 39, 131, 40, 42, 43, 44, 91, 45, 46, 47, 210, 48, 49, 50, 212, 110, 103, 52, 53, 54, 213, 211, 55, 141, 56, 214
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listen;
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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 1 of "1" and the 1 of "10";
1 digit between the 1 of "10" and the 1 of "12";
1 digit between the 1 of "12" and the first 1 of "11";
0 digit between the two 1s of "11";
1 digit between the last 1 of "11" and the 1 of "13";
2 digits between the 1 of "13" and the 1 of "14";
1 digit between the 1 of "14" and the 1 of "15";
1 digit between the 1 of "15" and the 1 of "16";
2 digits between the 1 of "16" and the 1 of "17";
1 digit between the 1 of "17" and the 1 of "18";
3 digits between the 1 of "18" and the 1 of "19";
3 digits between the 1 of "19" and the first 1 of "101";
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 1s.
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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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