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%I #14 Dec 08 2018 15:08:35
%S 12,121,1,2,21,11,122,22,111,1111,1222,222,211,2111,11111,111112,
%T 12222,2222,2221,221,1211,12111,111111,1111111,1111121,1112,22222,
%U 122222,222222,2222221,1221,2211,121112,21112,11111111,111111111,1111111111,11111111111,11121
%N To concatenate all terms, to concatenate the odd rank terms or to concatenate the even rank terms produces the same result.
%C The sequence starts with a(1) = 12 and is always extended with the smallest integer not yet present and not leading to a contradiction.
%C This is the lexicographically first sequence having this property, except the trivial 1, 11, 111, 1111, 11111,...
%C Trying a(1) = 10 gives a sequence with terms having leading zeroes -- which is not admitted.
%C All terms belong to A007931. - _Rémy Sigrist_, Dec 08 2018
%H Rémy Sigrist, <a href="/A299823/b299823.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A299823/a299823.png">Colored logarithmic scatterplot of the first 100000 terms</a>
%H Rémy Sigrist, <a href="/A299823/a299823.pl.txt">Perl program for A299823</a>
%e The first five terms of the sequence are:
%e 12,121,1,2,21
%e The first five odd-ranked terms are:
%e 12,1,21,122,111
%e The first five even-ranked terms are:
%e 121,2,11,22,1111
%e ... and we see that those three partitions start with the same concatenation:
%e 121211221...
%o (Perl) See Links section.
%Y Cf. A007931.
%K nonn,base,look
%O 1,1
%A _Eric Angelini_, Feb 19 2018
%E More terms from _Rémy Sigrist_, Dec 08 2018
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