Alon Vinkler - cp's OEIS frontend

User: Alon Vinkler

Alon Vinkler has authored 3 sequences.

A360703 Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 3 which is not already in the sequence.

1, 3, 9, 27, 67, 187, 129, 43, 41, 121, 17, 37, 97, 277, 677, 1877, 1297, 199, 133, 111, 113, 119, 139, 339, 313, 311, 331, 131, 191, 193, 393, 333, 399, 999, 933, 911, 913, 919, 319, 357, 157, 57, 19, 13, 11, 31, 33, 39, 99, 93, 91, 271, 273, 279, 679, 673, 671, 1871, 1291, 197, 137, 117, 151, 51, 53, 59, 159, 153

Offset: 0

Alon Vinkler, Feb 16 2023

At a given term t, the Choix de Bruxelles with factor 3 can choose to multiply any decimal digit substring (not starting 0) of t by 3 or divide by 3 if that substring is divisible by 3.
These choices on substrings give various possible next values and here take the smallest not yet in the sequence.
The sequence can be finite if the only choices we have are already in the sequence, but this has not been found in the first 1125299 terms.

			Below, square brackets [] represent multiplication by 3(e.g., [4] = 12); curly brackets {} represent division by 3 (e.g., {6} = 2); digits outside the brackets are not affected by the multiplication or division (e.g., 1[3] = 19 and 1{18} = 16).
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] = 3
 3 --> [3] = 9
 9 --> [9]= 27
 27--> [2]7 = 67
 67--> [6]7= 187
 187 --> 1{87}=129
 129 --> {129} = 43
 ... and so on.

Alon Vinkler, Table of n, a(n) for n = 0..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 [math.NT], 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.
Alon Vinkler, C# Program

Cf. A323286, A358708, A360190.

A360190 Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 13 which is not already in the sequence.

Original entry on oeis.org

1, 13, 133, 1333, 13333, 133333, 1333333, 125641, 1256413, 12564133, 1197241, 117481, 9037, 90391, 9031, 90313, 903133, 90241, 902413, 9024133, 90241333, 6941641, 693241, 6932413, 69324133, 6717241, 671557, 65557, 5557, 55591, 5431, 54313, 543133, 54241

Offset: 0

Alon Vinkler, Jan 29 2023

At a given term t, the Choix de Bruxelles with factor 13 can choose to multiply any decimal digit substring (not starting 0) of t by 13, or divide by 13 if that substring is divisible by 13.
These choices on substrings give various possible next values and here take the smallest not yet in the sequence.
The sequence is finite and ends at a(6851) = 7, since the sole next Choix there is multiplication by 13 to 91, but 91 is already in the sequence at the preceding a(6850) = 91.

			Below, square brackets [] represent multiplication by 13 (e.g., [4] = 52); curly brackets {} represent division by 13 (e.g., {26} = 2); digits outside the brackets are not affected by the multiplication or division (e.g., 1[3] = 139 and 1{169} = 113).
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] = 13
 13 --> [1]3 = 133
 133 --> [1]33 = 1333
 1333 --> [1]333 = 13333
 13333 --> [1]3333 = 133333
 133333 --> [1]33333 = 1333333
 1333333 --> 1{333333} = 125641
 ... and so on.

Alon Vinkler, Table of n, a(n) for n = 0..6851
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.
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane,, "Choix de Bruxelles": A New Operation on Positive Integers, Local copy.
Alon Vinkler, C# Program

Cf. A358708 (steps by factor 2), A323286 (Choix with factor 2).

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

Original entry on oeis.org

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

Alon Vinkler, Nov 26 2022

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.

			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.

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.
Eric Angelini, Lars Blomberg, Charlie Neder, Remy Sigrist, and N. J. A. Sloane,, "Choix de Bruxelles": A New Operation on Positive Integers, Local copy.
Alon Vinkler, C# Program

Cf. A323460, A307635, A323286, A323454.

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User: Alon Vinkler

A360703 Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 3 which is not already in the sequence.

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A360190 Starting from 1, successively take the smallest "Choix de Bruxelles" with factor 13 which is not already in the sequence.

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

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