A303157 Lexicographically earliest sequence of distinct terms such that the successive quantities of digits between two successive 2s are given by the succession of the sequence's digits itself.

0, 1, 2, 20, 21, 3, 23, 4, 22, 5, 6, 24, 25, 7, 8, 26, 9, 27, 10, 28, 11, 12, 13, 29, 32, 14, 15, 42, 16, 17, 18, 200, 201, 19, 203, 204, 30, 52, 31, 33, 34, 62, 35, 36, 37, 38, 205, 206, 39, 40, 207, 41, 43, 44, 72, 45, 208, 46, 47, 82, 92, 209, 210, 48, 49, 50, 202, 120, 211, 212, 51, 121

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 2 of "2" and the 2 of "20";
1 digit  between the 2 of "20" and the 2 of "21";
2 digits between the 2 of "21" and the 2 of "23";
2 digits between the 2 of "23" and the first 2 of "22";
0 digit  between the 2s of "22";
2 digits between the last 2 of "22" and the 2 of "24";
1 digit  between the 2 of "24" and the 2 of "25";
3 digits between the 2 of "25" and the 2 of "26";
2 digits between the 2 of "26" and the 2 of "27";
3 digits between the 2 of "27" and the 2 of "28";
4 digits between the 2 of "28" and the 2 of "12";
2 digits between the 2 of "12" and the 2 of "29";
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 2s.

Crossrefs

Cf. A303151 for the same idea with 1s as chunk's separators, A303158 with 3s, A302943 with 4s, A303163 with 5s, A303164 with 6s, A303166 with 7s, A303167 with 8s and A303171 with 9s.

Sequence in context: A075031 A273466 A278938 * A338994 A217394 A072998

Adjacent sequences: A303154 A303155 A303156 * A303158 A303159 A303160

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 19 2018

Status

approved