A360703 Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 3 which is not already in the sequence.

1, 3, 9, 27, 67, 187, 129, 43, 41, 121, 17, 37, 97, 277, 677, 1877, 1297, 199, 133, 111, 113, 119, 139, 339, 313, 311, 331, 131, 191, 193, 393, 333, 399, 999, 933, 911, 913, 919, 319, 357, 157, 57, 19, 13, 11, 31, 33, 39, 99, 93, 91, 271, 273, 279, 679, 673, 671, 1871, 1291, 197, 137, 117, 151, 51, 53, 59, 159, 153

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

Cf. A323286, A358708, A360190.

Sequence in context: A161712 A280466 A137368 * A191007 A036215 A103828

Adjacent sequences: A360700 A360701 A360702 * A360704 A360705 A360706

Keyword

nonn,base

Author

Alon Vinkler, Feb 16 2023

Status

approved