A358708 Starting from 1, successively take the smallest "Choix de Bruxelles" (A323286) which is not already in the sequence.

1, 2, 4, 8, 16, 13, 23, 26, 46, 43, 83, 86, 166, 133, 136, 68, 34, 17, 27, 47, 87, 167, 137, 174, 172, 171, 271, 272, 236, 118, 19, 29, 49, 89, 169, 139, 178, 278, 239, 269, 469, 439, 478, 474, 237, 267, 467, 437, 837, 867, 1667, 1337, 1367, 687, 347, 177, 277, 477, 877, 1677, 1377, 1747, 1727, 1717, 1734, 1732, 866, 433, 233, 263, 163, 323, 313, 316, 38, 76, 73, 143, 123, 63, 33, 36, 18, 9

Offset

0,2

Comments

The Choix de Bruxelles doubles or halves some decimal digit substring and rows of A323286 are all ways this can be done.

So a(n) is the smallest term of the row a(n-1) of A323286 which is not among {a(0..n-1)}.

The sequence is finite since having reached 18 -> 9 the sole Choix for 9 would be back to 18, which is already in the sequence.

Links

Table of n, a(n) for n=0..83.

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 [math.NT], Feb 2019; Fib. Quart. 57:3 (2019), 195-200.

Alon Vinkler, C# Program

Example

Below, square brackets [] represent multiplication by 2 (e.g., [6] = 12); curly brackets {} represent division by 2 (e.g., {6} = 3); digits outside the brackets are not affected by the multiplication or division (e.g., 1[6] = 112 and 1{14} = 17).
We begin with 1 and, at each step, we go to the smallest number possible that hasn't yet appeared in the sequence:
 1 --> [1]  =  2
 2 --> [2]  =  4
 4 --> [4]  =  8
 8 --> [8]  = 16
 16 --> 1{6} = 13
 13 --> [1]3 = 23
 23 --> 2[3] = 26
 26 --> [2]6 = 46
 ... and so on.

Prog

(C#) //(see in links)

Crossrefs

Cf. A323460, A307635, A323286, A323454.

Sequence in context: A208278 A036120 A334629 * A108565 A066005 A066600

Adjacent sequences: A358705 A358706 A358707 * A358709 A358710 A358711

Keyword

nonn,easy,base,fini,full

Author

Alon Vinkler, Nov 26 2022

Status

approved