A323484 -id:A323484 - cp's OEIS frontend

A323464 Values of n at which A323484 reaches a new record.

1, 2, 3, 6, 20, 40, 80, 1975, 3999, 15995, 39999

Offset: 1

N. J. A. Sloane, Jan 23 2019

The corresponding numbers of steps are 0, 1, 11, 12, 13, 14, 15, 16, 17.

			a(4)=20 refers to the fact that it takes 13 steps to reach 100 from 5 using the Choix de Bruxelles (version 2) operation, and all multiples of 5 less than 100 can be reached from 5 in fewer than 13 steps.

Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, "Choix de Bruxelles": A New Operation on Positive Integers, arXiv:1902.01444, Feb 2019; Fib. Quart. 57:3 (2019), 195-200.
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane,, "Choix de Bruxelles": A New Operation on Positive Integers, Local copy.

Cf. A323286, A323460, A323454, A323484.

a(10) from Michael S. Branicky, Oct 05 2024

a(11) from Michael S. Branicky, Oct 11 2024

A323454 Minimal number of steps to reach n from 1 using "Choix de Bruxelles", version 2 (cf. A323460), or -1 if n cannot be reached.

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Jan 15 2019

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.

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

			Examples of optimal ways to reach 1,2,3,...:
1
1, 2
1, 2, 4, 8, 16, 112, 56, 28, 14, 12, 6, 3
1, 2, 4
5 cannot be reached, ends in 0 or 5
1, 2, 4, 8, 16, 112, 56, 28, 14, 12, 6
1, 2, 4, 8, 16, 112, 56, 28, 14, 7
1, 2, 4, 8,
1, 2, 4, 8, 16, 112, 56, 28, 18, 9.
10 cannot be reached, ends in 0 or 5
1, 2, 4, 8, 16, 112, 56, 28, 24, 22, 11
1, 2, 4, 8, 16, 112, 56, 28, 14, 12
1, 2, 4, 8, 16, 13
1, 2, 4, 8, 16, 112, 56, 28, 14
15 cannot be reached, ends in 0 or 5
1, 2, 4, 8, 16
1, 2, 4, 8, 16, 32, 34, 17
1, 2, 4, 8, 16, 112, 56, 28, 18
1, 2, 4, 8, 16, 32, 34, 38, 19
20 cannot be reached, ends in 0 or 5
...

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane, "Choix de Bruxelles": A New Operation on Positive Integers, arXiv:1902.01444, Feb 2019; Fib. Quart. 57:3 (2019), 195-200.
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane,, "Choix de Bruxelles": A New Operation on Positive Integers, Local copy.
Brady Haran and N. J. A. Sloane, The Brussels Choice, Numberphile video (2020)
N. J. A. Sloane, Coordination Sequences, Planing Numbers, and Other Recent Sequences (II), Experimental Mathematics Seminar, Rutgers University, Jan 31 2019, Part I, Part 2, Slides. (Mentions this sequence)

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

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

More terms from Rémy Sigrist, Jan 15 2019

cp's OEIS Frontend

A323464 Values of n at which A323484 reaches a new record.

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