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

1,2

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

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

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

Sequence in context: A155890 A213969 A199986 * A077410 A211029 A225188

Adjacent sequences: A336525 A336526 A336527 * A336529 A336530 A336531

Keyword

nonn,base

Author

Rémy Sigrist, Jul 24 2020

Status

approved