OFFSET
0,2
COMMENTS
At a given term t, the Choix de Bruxelles with factor 3 can choose to multiply any decimal digit substring (not starting 0) of t by 3 or divide by 3 if that substring is divisible by 3.
These choices on substrings give various possible next values and here take the smallest not yet in the sequence.
The sequence can be finite if the only choices we have are already in the sequence, but this has not been found in the first 1125299 terms.
LINKS
Alon Vinkler, Table of n, a(n) for n = 0..10000
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, "Choix de Bruxelles": A New Operation on Positive Integers, arXiv:1902.01444 [math.NT], Feb 2019; Fib. Quart. 57:3 (2019), 195-200.
Alon Vinkler, C# Program
EXAMPLE
Below, square brackets [] represent multiplication by 3(e.g., [4] = 12); curly brackets {} represent division by 3 (e.g., {6} = 2); digits outside the brackets are not affected by the multiplication or division (e.g., 1[3] = 19 and 1{18} = 16).
We begin with 1 and, at each step, we go to the smallest number possible that hasn't yet appeared in the sequence:
1 --> [1] = 3
3 --> [3] = 9
9 --> [9]= 27
27--> [2]7 = 67
67--> [6]7= 187
187 --> 1{87}=129
129 --> {129} = 43
... and so on.
PROG
(C#) // See Links
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Alon Vinkler, Feb 16 2023
STATUS
approved