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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.
3
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jul 24 2020
STATUS
approved