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

%I A360703 #26 Jan 09 2025 13:04:40
%S A360703 1,3,9,27,67,187,129,43,41,121,17,37,97,277,677,1877,1297,199,133,111,
%T A360703 113,119,139,339,313,311,331,131,191,193,393,333,399,999,933,911,913,
%U A360703 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
%N A360703 Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 3 which is not already in the sequence.
%C A360703 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.
%C A360703 These choices on substrings give various possible next values and here take the smallest not yet in the sequence.
%C A360703 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.
%H A360703 Alon Vinkler, <a href="/A360703/b360703.txt">Table of n, a(n) for n = 0..10000</a>
%H A360703 Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, <a href="http://arxiv.org/abs/1902.01444">"Choix de Bruxelles": A New Operation on Positive Integers</a>, arXiv:1902.01444 [math.NT], Feb 2019; Fib. Quart. 57:3 (2019), 195-200.
%H A360703 Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane,, <a href="/A307635/a307635.pdf">"Choix de Bruxelles": A New Operation on Positive Integers</a>, Local copy.
%H A360703 Alon Vinkler, <a href="/A360703/a360703_1.txt">C# Program</a>
%e A360703 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).
%e A360703 We begin with 1 and, at each step, we go to the smallest number possible that hasn't yet appeared in the sequence:
%e A360703  1 --> [1] = 3
%e A360703  3 --> [3] = 9
%e A360703  9 --> [9]= 27
%e A360703  27--> [2]7 = 67
%e A360703  67--> [6]7= 187
%e A360703  187 --> 1{87}=129
%e A360703  129 --> {129} = 43
%e A360703  ... and so on.
%o A360703 (C#) // See Links
%Y A360703 Cf. A323286, A358708, A360190.
%K A360703 nonn,base
%O A360703 0,2
%A A360703 _Alon Vinkler_, Feb 16 2023