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A323454
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Minimal number of steps to reach n from 1 using "Choix de Bruxelles", version 2 (cf. A323460), or -1 if n cannot be reached.
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10
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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
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OFFSET
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1,3
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COMMENTS
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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).
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LINKS
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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)
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EXAMPLE
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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
...
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CROSSREFS
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For variants of the Choix de Bruxelles operation, see A337321 and A337357.
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KEYWORD
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sign,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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