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Pick any pair of "0" digits in the sequence. Those two "0"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.
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%I #10 Dec 27 2023 12:03:35

%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,

%T 26,27,28,29,31,30,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,

%U 49,51,52,53,50,54,55,56,57,58,59,61,62,63,64,65,60,66,67,68,69,71,70,72,73,74,75,76,77,78

%N Pick any pair of "0" digits in the sequence. Those two "0"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 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 Eric Angelini, <a href="/A273888/b273888.txt">Table of n, a(n) for n = 1..1011</a>

%H See oeis.org/A273376 for the equivalent sequence dealing with digit-"1" pairs instead of "0"

%K nonn,base

%O 1,3

%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jun 02 2016