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A336528 a(1) = 1; a(2) = 2; for n > 2, a(n) is the least number > a(n-1) whose decimal representation is uniquely the concatenation of the decimal representations of two distinct earlier terms.

%I A336528 #20 Oct 28 2023 11:41:03
%S A336528 1,2,12,21,112,122,211,221,1112,1121,1211,1222,2111,2122,2212,2221,
%T A336528 11112,11122,11221,11222,12211,12222,21111,21122,22111,22112,22211,
%U A336528 22221,111112,111121,111212,112112,112121,112122,112212,121111,121122,121211,121222,122122
%N A336528 a(1) = 1; a(2) = 2; for n > 2, a(n) is the least number > a(n-1) whose decimal representation is uniquely the concatenation of the decimal representations of two distinct earlier terms.
%C A336528 This sequence is inspired by Ulam sequence (A002858).
%C A336528 All terms belong to A007931.
%C A336528 Applying the mapping 1 -> 0, 2 -> 1 to the decimal representations of the terms of this sequence gives the sequence U({0, 1}) described in the article by Bade et al. in Links section. - _Rémy Sigrist_, Aug 08 2020
%H A336528 Rémy Sigrist, <a href="/A336528/b336528.txt">Table of n, a(n) for n = 1..15616</a> (terms < 10^15)
%H A336528 Tej Bade, Kelly Cui, Antoine Labelle, and Deyuan Li, <a href="https://arxiv.org/abs/2008.02762">Ulam Sets in New Settings</a>, arXiv:2008.02762 [math.CO], 2020. See also <a href="http://math.colgate.edu/~integers/u102/u102.pdf">Integers</a> (2020) Vol. 20, #A102.
%H A336528 Rémy Sigrist, <a href="/A336528/a336528.gp.txt">PARI program for A336528</a>
%e A336528 The first terms, alongside A007931 and the corresponding concatenations, are:
%e A336528   n   a(n)  A007931  concatenations
%e A336528   --  ----  -------  --------------
%e A336528    1     1        1
%e A336528    2     2        2
%e A336528                  11
%e A336528    3    12       12  1|2
%e A336528    4    21       21  2|1
%e A336528                  22
%e A336528                 111  1|11, 11|1
%e A336528    5   112      112  1|12
%e A336528                 121  1|21, 12|1
%e A336528    6   122      122  12|2
%e A336528    7   211      211  21|1
%e A336528                 212  2|12, 21|2
%e A336528    8   221      221  2|21
%e A336528                 222
%e A336528                1111
%e A336528    9  1112     1112  1|112
%e A336528   10  1121     1121  112|1
%o A336528 (PARI) See Links section.
%Y A336528 Cf. A002858, A007931, A336527 (binary variant).
%K A336528 nonn,base
%O A336528 1,2
%A A336528 _Rémy Sigrist_, Jul 24 2020