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A318225 Lexicographically earliest sequence of positive terms such that the concatenation of two consecutive terms is always unique.

%I A318225 #10 Aug 24 2018 17:20:35
%S A318225 1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,1,10,1,11,2,2,3,2,4,2,5,2,6,2,7,2,
%T A318225 8,2,9,2,10,2,11,3,3,4,3,5,3,6,3,7,3,8,3,9,3,10,3,11,4,4,5,4,6,4,7,4,
%U A318225 8,4,9,4,10,4,11,5,5,6,5,7,5,8,5,9,5,10,5
%N A318225 Lexicographically earliest sequence of positive terms such that the concatenation of two consecutive terms is always unique.
%C A318225 In other words, for any distinct i and j, A066686(a(i), a(i+1)) <> A066686(a(j), a(j+1)).
%C A318225 The sequence b such that for any n > 0, b(n) = A066686(a(n), a(n+1)), satisfies b(n) = A303446(n+1) for n = 1..116 and b(117) <> A303446(118).
%C A318225 The sequence contains long runs of consecutive terms where one term out of two equals 1.
%H A318225 Rémy Sigrist, <a href="/A318225/b318225.txt">Table of n, a(n) for n = 1..10000</a>
%H A318225 Rémy Sigrist, <a href="/A318225/a318225.png">Logarithmic density plot of the first 300000000 terms</a>
%H A318225 Rémy Sigrist, <a href="/A318225/a318225.txt">C++ program for A318225</a>
%e A318225 The first terms, alongside the concatenation of a(n) and of a(n+1), are:
%e A318225   n  a(n)   A066686(a(n), a(n+1))
%e A318225   -- ----   ---------------------
%e A318225    1    1    11
%e A318225    2    1    12
%e A318225    3    2    21
%e A318225    4    1    13
%e A318225    5    3    31
%e A318225    6    1    14
%e A318225    7    4    41
%e A318225    8    1    15
%e A318225    9    5    51
%e A318225   10    1    16
%e A318225   11    6    61
%e A318225   12    1    17
%e A318225   13    7    71
%e A318225   14    1    18
%e A318225   15    8    81
%e A318225   16    1    19
%e A318225   17    9    91
%e A318225   18    1   110
%e A318225   19   10   101
%e A318225   20    1   111
%e A318225   21   11   112
%e A318225   22    2    22
%e A318225   23    2    23
%e A318225   24    3    32
%e A318225   25    2    24
%o A318225 (C++) See Links section.
%Y A318225 Cf. A066686, A303446.
%K A318225 nonn,base,look
%O A318225 1,3
%A A318225 _Rémy Sigrist_, Aug 21 2018