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A323460
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Choix de Bruxelles, version 2: irregular table read by rows in which row n lists all the legal numbers that can be reached by halving or doubling some substring of the decimal expansion of n (including the empty string).
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12
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1, 2, 1, 2, 4, 3, 6, 2, 4, 8, 5, 10, 3, 6, 12, 7, 14, 4, 8, 16, 9, 18, 5, 10, 20, 11, 12, 21, 22, 6, 11, 12, 14, 22, 24, 13, 16, 23, 26, 7, 12, 14, 18, 24, 28, 15, 25, 30, 110, 8, 13, 16, 26, 32, 112, 17, 27, 34, 114, 9, 14, 18, 28, 36, 116, 19, 29, 38
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OFFSET
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1,2
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COMMENTS
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The differs from the first version (in A323286) in that now n can be reached from n (by using the empty string).
This slight modification of the definition makes the analysis simpler.
The number of numbers that can be reached from n in one step is A323287(n)+1.
The minimal number of steps to reach n starting at 1 is still given by A323454.
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LINKS
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Table of n, a(n) for n=1..68.
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 Neil Sloane, The Brussels Choice, Numberphile video (2020)
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EXAMPLE
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Rows 1 through 20 are:
1, 2,
1, 2, 4,
3, 6,
2, 4, 8,
5, 10,
3, 6, 12,
7, 14,
4, 8, 16,
9, 18,
5, 10, 20,
11, 12, 21, 22,
6, 11, 12, 14, 22, 24,
13, 16, 23, 26,
7, 12, 14, 18, 24, 28,
15, 25, 30, 110,
8, 13, 16, 26, 32, 112,
17, 27, 34, 114,
9, 14, 18, 28, 36, 116,
19, 29, 38, 118,
10, 20, 40
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CROSSREFS
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Cf. A323286, A323287, A323453, A323454.
Sequence in context: A323465 A124904 A187500 * A129144 A295313 A105022
Adjacent sequences: A323457 A323458 A323459 * A323461 A323462 A323463
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KEYWORD
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nonn,base,tabf
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AUTHOR
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N. J. A. Sloane, Jan 22 2019
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STATUS
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approved
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