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Pick any pair of "8" digits in the sequence. Those two "8"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 #12 Jun 09 2016 08:36:28

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

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

%N Pick any pair of "8" digits in the sequence. Those two "8"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="/A273886/b273886.txt">Table of n, a(n) for n = 1..1011</a>

%Y See A273376 for the equivalent sequence dealing with digit-"1" pairs instead of "8"

%K nonn,base

%O 1,3

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