A303158 Lexicographically earliest sequence of distinct terms such that the successive quantities of digits between two successive 3s are given by the succession of the sequence's digits itself.

0, 1, 2, 3, 30, 31, 4, 32, 5, 6, 34, 7, 8, 33, 9, 10, 35, 36, 11, 13, 12, 23, 14, 37, 15, 16, 38, 17, 18, 43, 19, 53, 20, 21, 39, 22, 24, 25, 300, 26, 27, 28, 301, 63, 29, 73, 40, 41, 42, 44, 83, 93, 302, 130, 45, 46, 304, 131, 47, 48, 132, 303, 134, 49, 313, 50, 305, 306, 135, 307, 51, 308

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..1503

Example

There are:
0 digit  between the 3 of "3" and the 3 of "30";
1 digit  between the 3 of "30" and the 3 of "31";
2 digits between the 3 of "31" and the 3 of "32";
3 digits between the 3 of "32" and the 3 of "34";
3 digits between the 3 of "34" and the first 3 of "33";
0 digit  between the 3s of "33";
3 digits between the last 3 of "33" and the 3 of "35";
1 digit  between the 3 of "35" and the 3 of "36";
4 digits between the 3 of "36" and the 3 of "13";
3 digits between the 3 of "13" and the 3 of "23";
2 digits between the 3 of "23" and the 3 of "37";
5 digits between the 3 of "37" and the 3 of "38";
6 digits between the 3 of "38" and the 3 of "43";
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 3s.

Crossrefs

Cf. A303151 for the same idea with 1s as chunk's separators, and A303157 with 2s. Cf. A303151 for the same idea with 1s as chunk's separators, A303157 with 2s, A302943 with 4s, A303163 with 5s, A303164 with 6s, A303166 with 7s, A303167 with 8s and A303171 with 9s.

Sequence in context: A278048 A273467 A278861 * A024631 A032814 A233587

Adjacent sequences: A303155 A303156 A303157 * A303159 A303160 A303161

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 19 2018

Status

approved