A360190 - OEIS

A360190

Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 13 which is not already in the sequence.

%I #41 May 10 2023 07:27:44

%S 1,13,133,1333,13333,133333,1333333,125641,1256413,12564133,1197241,

%T 117481,9037,90391,9031,90313,903133,90241,902413,9024133,90241333,

%U 6941641,693241,6932413,69324133,6717241,671557,65557,5557,55591,5431,54313,543133,54241

%N Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 13 which is not already in the sequence.

%C At a given term t, the Choix de Bruxelles with factor 13 can choose to multiply any decimal digit substring (not starting 0) of t by 13, or divide by 13 if that substring is divisible by 13.

%C These choices on substrings give various possible next values and here take the smallest not yet in the sequence.

%C The sequence is finite and ends at a(6851) = 7, since the sole next Choix there is multiplication by 13 to 91, but 91 is already in the sequence at the preceding a(6850) = 91.

%H Alon Vinkler, <a href="/A360190/b360190.txt">Table of n, a(n) for n = 0..6851</a>

%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="/A360190/a360190_2.txt">C# Program</a>

%e Below, square brackets [] represent multiplication by 13 (e.g., [4] = 52); curly brackets {} represent division by 13 (e.g., {26} = 2); digits outside the brackets are not affected by the multiplication or division (e.g., 1[3] = 139 and 1{169} = 113).

%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] = 13

%e 13 --> [1]3 = 133

%e 133 --> [1]33 = 1333

%e 1333 --> [1]333 = 13333

%e 13333 --> [1]3333 = 133333

%e 133333 --> [1]33333 = 1333333

%e 1333333 --> 1{333333} = 125641

%e ... and so on.

%o (C#) // See Links

%Y Cf. A358708 (steps by factor 2), A323286 (Choix with factor 2).

%K nonn,base,fini,full

%O 0,2

%A _Alon Vinkler_, Jan 29 2023