login
Smallest number that can be obtained by starting with 1 and applying "Choix de Bruxelles (version 2)" (see A323460) n times without backtracking or repeating.
0

%I #25 Jan 09 2025 13:05:29

%S 1,2,4,8,16,13,23,17,14,7,6,3,99,369,999,1999,9879,19979

%N Smallest number that can be obtained by starting with 1 and applying "Choix de Bruxelles (version 2)" (see A323460) n times without backtracking or repeating.

%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 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.

%F A323454(a(n)) = n by definition.

%e a(0)-a(4) = 1,2,4,8,16 by applying 0,1,2,3,4 steps: 1->2->4->8->16.

%e a(5) = 13 by applying 5 steps: 1->2->4->8->16->13 (halve the 6 in 16).

%e a(11) = 3 by applying 11 steps to reach 3 from 1.

%Y Cf. A323454, A323460.

%K nonn,base,more

%O 0,2

%A _Philip C. Ritchey_, Sep 09 2020

%E a(17) from _Michael S. Branicky_, Oct 01 2024