A323454 - OEIS

%I #29 Jan 09 2025 13:00:16

%S 0,1,11,2,-1,10,9,3,9,-1,10,9,5,8,-1,4,7,8,8,-1,10,9,6,8,-1,5,8,7,9,

%T -1,6,5,10,6,-1,9,9,7,9,-1,11,10,7,9,-1,6,9,8,10,-1,7,6,7,7,-1,6,7,8,

%U 8,-1,7,6,11,6,-1,10,10,7,10,-1,8,8,9,8,-1,8,11,8

%N Minimal number of steps to reach n from 1 using "Choix de Bruxelles", version 2 (cf. A323460), or -1 if n cannot be reached.

%C This is equally the minimal number of steps to reach n from 1 using "Choix de Bruxelles", version 1 (cf. A323286), or -1 if n cannot be reached.

%C n cannot be reached if its final digit is 0 or 5, but all other numbers can be reached (see comments in A323286).

%H Rémy Sigrist, <a href="/A323454/b323454.txt">Table of n, a(n) for n = 1..10000</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, 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.

%H Brady Haran and N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=AeqK96UX3rA">The Brussels Choice</a>, Numberphile video (2020)

%H N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, <a href="https://vimeo.com/314786942">Part I</a>, <a href="https://vimeo.com/314790822">Part 2</a>, <a href="https://oeis.org/A320487/a320487.pdf">Slides.</a> (Mentions this sequence)

%e Examples of optimal ways to reach 1,2,3,...:

%e 1

%e 1, 2

%e 1, 2, 4, 8, 16, 112, 56, 28, 14, 12, 6, 3

%e 1, 2, 4

%e 5 cannot be reached, ends in 0 or 5

%e 1, 2, 4, 8, 16, 112, 56, 28, 14, 12, 6

%e 1, 2, 4, 8, 16, 112, 56, 28, 14, 7

%e 1, 2, 4, 8,

%e 1, 2, 4, 8, 16, 112, 56, 28, 18, 9.

%e 10 cannot be reached, ends in 0 or 5

%e 1, 2, 4, 8, 16, 112, 56, 28, 24, 22, 11

%e 1, 2, 4, 8, 16, 112, 56, 28, 14, 12

%e 1, 2, 4, 8, 16, 13

%e 1, 2, 4, 8, 16, 112, 56, 28, 14

%e 15 cannot be reached, ends in 0 or 5

%e 1, 2, 4, 8, 16

%e 1, 2, 4, 8, 16, 32, 34, 17

%e 1, 2, 4, 8, 16, 112, 56, 28, 18

%e 1, 2, 4, 8, 16, 32, 34, 38, 19

%e 20 cannot be reached, ends in 0 or 5

%e ...

%Y Cf. A323286-A323289, A323453, A323484, A323460.

%Y For variants of the Choix de Bruxelles operation, see A337321 and A337357.

%K sign,base,changed

%O 1,3

%A _N. J. A. Sloane_, Jan 15 2019

%E More terms from _Rémy Sigrist_, Jan 15 2019