A303151 - OEIS

%I #19 Apr 21 2018 06:21:21

%S 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,

%T 41,51,24,25,26,100,27,121,28,29,30,61,71,32,33,34,35,102,36,81,37,38,

%U 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

%N 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.

%C 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

%C This sequence is a permutation of the numbers >= 0.

%H Jean-Marc Falcoz, <a href="/A303151/b303151.txt">Table of n, a(n) for n = 1..2202</a>

%e There are:

%e 0 digit  between the 1 of "1" and the 1 of "10";

%e 1 digit  between the 1 of "10" and the 1 of "12";

%e 1 digit  between the 1 of "12" and the first 1 of "11";

%e 0 digit  between the two 1s of "11";

%e 1 digit  between the last 1 of "11" and the 1 of "13";

%e 2 digits between the 1 of "13" and the 1 of "14";

%e 1 digit  between the 1 of "14" and the 1 of "15";

%e 1 digit  between the 1 of "15" and the 1 of "16";

%e 2 digits between the 1 of "16" and the 1 of "17";

%e 1 digit  between the 1 of "17" and the 1 of "18";

%e 3 digits between the 1 of "18" and the 1 of "19";

%e 3 digits between the 1 of "19" and the first 1 of "101";

%e etc.

%e 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.

%Y 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.

%K nonn,base

%O 1,3

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Apr 19 2018