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%I #85 May 10 2023 07:27:08
%S 1,2,4,8,16,13,23,26,46,43,83,86,166,133,136,68,34,17,27,47,87,167,
%T 137,174,172,171,271,272,236,118,19,29,49,89,169,139,178,278,239,269,
%U 469,439,478,474,237,267,467,437,837,867,1667,1337,1367,687,347,177,277,477,877,1677,1377,1747,1727,1717,1734,1732,866,433,233,263,163,323,313,316,38,76,73,143,123,63,33,36,18,9
%N Starting from 1, successively take the smallest "Choix de Bruxelles" (A323286) which is not already in the sequence.
%C The Choix de Bruxelles doubles or halves some decimal digit substring and rows of A323286 are all ways this can be done.
%C So a(n) is the smallest term of the row a(n-1) of A323286 which is not among {a(0..n-1)}.
%C The sequence is finite since having reached 18 -> 9 the sole Choix for 9 would be back to 18, which is already in the sequence.
%H 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 Alon Vinkler, <a href="/A358708/a358708_1.txt">C# Program</a>
%e Below, square brackets [] represent multiplication by 2 (e.g., [6] = 12); curly brackets {} represent division by 2 (e.g., {6} = 3); digits outside the brackets are not affected by the multiplication or division (e.g., 1[6] = 112 and 1{14} = 17).
%e We begin with 1 and, at each step, we go to the smallest number possible that hasn't yet appeared in the sequence:
%e 1 --> [1] = 2
%e 2 --> [2] = 4
%e 4 --> [4] = 8
%e 8 --> [8] = 16
%e 16 --> 1{6} = 13
%e 13 --> [1]3 = 23
%e 23 --> 2[3] = 26
%e 26 --> [2]6 = 46
%e ... and so on.
%o (C#) //(see in links)
%Y Cf. A323460, A307635, A323286, A323454.
%K nonn,easy,base,fini,full
%O 0,2
%A _Alon Vinkler_, Nov 26 2022