A336528 - OEIS

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 #20 Oct 28 2023 11:41:03

%S 1,2,12,21,112,122,211,221,1112,1121,1211,1222,2111,2122,2212,2221,

%T 11112,11122,11221,11222,12211,12222,21111,21122,22111,22112,22211,

%U 22221,111112,111121,111212,112112,112121,112122,112212,121111,121122,121211,121222,122122

%N 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 This sequence is inspired by Ulam sequence (A002858).

%C All terms belong to A007931.

%C 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 Rémy Sigrist, <a href="/A336528/b336528.txt">Table of n, a(n) for n = 1..15616</a> (terms < 10^15)

%H 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 Rémy Sigrist, <a href="/A336528/a336528.gp.txt">PARI program for A336528</a>

%e The first terms, alongside A007931 and the corresponding concatenations, are:

%e n a(n) A007931 concatenations

%e -- ---- ------- --------------

%e 1 1 1

%e 2 2 2

%e 11

%e 3 12 12 1|2

%e 4 21 21 2|1

%e 22

%e 111 1|11, 11|1

%e 5 112 112 1|12

%e 121 1|21, 12|1

%e 6 122 122 12|2

%e 7 211 211 21|1

%e 212 2|12, 21|2

%e 8 221 221 2|21

%e 222

%e 1111

%e 9 1112 1112 1|112

%e 10 1121 1121 112|1

%o (PARI) See Links section.

%Y Cf. A002858, A007931, A336527 (binary variant).

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Jul 24 2020