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.

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

1,3

Comments

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).

Links

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.

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)

Example

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
...

Crossrefs

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

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

Sequence in context: A193925 A365644 A010190 * A261353 A087774 A322562

Adjacent sequences: A323451 A323452 A323453 * A323455 A323456 A323457

Keyword

sign,base

Author

N. J. A. Sloane, Jan 15 2019

Extensions

More terms from Rémy Sigrist, Jan 15 2019

Status

approved