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.

1, 2, 12, 21, 112, 122, 211, 221, 1112, 1121, 1211, 1222, 2111, 2122, 2212, 2221, 11112, 11122, 11221, 11222, 12211, 12222, 21111, 21122, 22111, 22112, 22211, 22221, 111112, 111121, 111212, 112112, 112121, 112122, 112212, 121111, 121122, 121211, 121222, 122122

Offset: 1

Author

Rémy Sigrist, Jul 24 2020

Keywords

• nonn
• base

Comments

This sequence is inspired by Ulam sequence (A002858).

All terms belong to A007931.

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

Examples

			The first terms, alongside A007931 and the corresponding concatenations, are:
  n   a(n)  A007931  concatenations
  --  ----  -------  --------------
   1     1        1
   2     2        2
                 11
   3    12       12  1|2
   4    21       21  2|1
                 22
                111  1|11, 11|1
   5   112      112  1|12
                121  1|21, 12|1
   6   122      122  12|2
   7   211      211  21|1
                212  2|12, 21|2
   8   221      221  2|21
                222
               1111
   9  1112     1112  1|112
  10  1121     1121  112|1
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..15616 (terms < 10^15)
• Tej Bade, Kelly Cui, Antoine Labelle, and Deyuan Li, Ulam Sets in New Settings, arXiv:2008.02762 [math.CO], 2020. See also Integers (2020) Vol. 20, #A102.
• Rémy Sigrist, PARI program for A336528

Crossrefs

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

Programs

PARI

See Links section.