A303164 Lexicographically earliest sequence of distinct terms such that the successive quantities of digits between two successive 6s are given by the succession of the sequence's digits itself.

0, 1, 2, 3, 4, 5, 6, 60, 61, 7, 62, 8, 9, 63, 10, 16, 11, 12, 26, 13, 14, 15, 64, 17, 18, 36, 65, 19, 20, 46, 56, 21, 22, 23, 76, 24, 25, 27, 67, 86, 28, 29, 30, 31, 68, 32, 33, 34, 35, 69, 37, 38, 96, 39, 160, 66, 161, 40, 41, 162, 606, 163, 164, 165, 42, 43, 167, 600, 168, 601, 44, 616, 45, 47, 169

Offset

1,3

Comments

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.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..1507

Example

There are:
0 digit  between the 6 of "6" and the 6 of "60";
1 digit  between the 6 of "60" and the 6 of "61";
2 digits between the 6 of "61" and the 6 of "62";
3 digits between the 6 of "62" and the 6 of "63";
4 digits between the 6 of "63" and the 6 of "16";
5 digits between the 6 of "16" and the 6 of "26";
6 digits between the 6 of "26" and the 6 of "64";
6 digits between the 6 of "64" and the 6 of "36";
0 digit  between the 6 of "36" and the 6 of "65";
6 digits between the 6 of "65" and the 6 of "46";
1 digit  between the 6 of "46" and the 6 of "56";
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 6s.

Crossrefs

Cf. A303151 for the same idea with 1s as chunk's separators, A303157 with 2s, A303158 with 3s, A302943 with 4s, A303163 with 5s, A303166 with 7s, A303167 with 8s and A303171 with 9s.

Sequence in context: A028428 A273473 A278941 * A024643 A166099 A004857

Adjacent sequences: A303161 A303162 A303163 * A303165 A303166 A303167

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 19 2018

Status

approved