A303151 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.

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

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..2202

Example

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.

Crossrefs

Cf. A303157 for the same idea with 2s 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: A365197 A284229 A078285 * A103618 A308781 A317180

Adjacent sequences: A303148 A303149 A303150 * A303152 A303153 A303154

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Apr 19 2018

Status

approved