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A273376 Pick any pair of "1" digits in the sequence. Those two "1"s are separated by k digits. This is the lexicographically earliest sequence of distinct terms in which all the resulting values of k are distinct.

%I A273376 #23 Jun 02 2016 16:08:56
%S A273376 0,1,2,3,4,5,6,7,8,9,10,11,20,21,22,23,24,25,26,27,12,28,29,13,30,32,
%T A273376 33,14,34,35,36,37,38,39,40,42,43,44,15,45,46,47,48,49,50,31,52,53,54,
%U A273376 55,41,56,57,58,59,60,62,63,64,65,66,67,68,69,70,72,73,74,75,51,76,77,78,79,80,82,83,84,85,86,87,88,89,61,90,92,93,94,95,96,97,98,99,200,202,203,204,205,206,201
%N A273376 Pick any pair of "1" digits in the sequence. Those two "1"s are separated by k digits. This is the lexicographically earliest sequence of distinct terms in which all the resulting values of k are distinct.
%C A273376 The sequence starts with a(1)=0. It is then always extended with the smallest integer not yet present and not leading to a contradiction (which would mean producing a value of k already seen).
%H A273376 Eric Angelini, <a href="/A273376/b273376.txt">Table of n, a(n) for n = 1..1011</a>
%e A273376 The ten "k"s in the starting segment here are different [0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21,] and respectively equal to 8,10,11,15,1,2,6,0,4,3.
%e A273376 Indeed, there are k=8 digits between [1] and the "1" of [10] which are 2,3,4,5,6,7,8,9; there are k=10 digits between [1] and the first "1" of [11] which are 2,3,4,5,6,7,8,9,1,0;  there are k=11 digits between [1] and the second "1" of [11] which are 2,3,4,5,6,7,8,9,1,0,1; there are k=15 digits between [1] and the "1" of [21] which are 2,3,4,5,6,7,8,9,1,0,1,1,2,0,2.
%e A273376 There is k=1 digit between the "1" of [10] and the first "1" of [11] which is 0; there are k=2 digits between the "1" of [10] and the second "1" of [11] which are 0 and 1; there are k=6 digits between the "1" of [10] and the "1" of [21] which are 0,1,1,2,0,2.
%e A273376 There are k=0 digits between the first "1" of [11] and the second "1" of [11]; there are k=4 digits between the first "1" of [11] and the "1" of [21] which are 1,2,0,2.
%e A273376 There are k=3 digits between the second "1" of [11] and the "1" of [21] which are 2,0 and 2.
%K A273376 nonn,base
%O A273376 1,3
%A A273376 _Eric Angelini_ and _Jean-Marc Falcoz_, May 30 2016