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A329233
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The time of the first counterclockwise step during the grasshopper procedure, or 0 if no counterclockwise steps occur.
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4
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0, 0, 2, 0, 4, 5, 4, 0, 4, 4, 6, 5, 8, 5, 5, 0, 13, 6, 10, 6, 6, 7, 12, 17, 7, 8, 7, 7, 16, 8, 16, 0, 8, 12, 8, 8, 20, 13, 9, 10, 25, 9, 22, 9, 9, 13, 24, 17, 10, 12, 11, 10, 28, 10, 10, 11, 12, 16, 30, 11, 32, 17, 11, 0, 11, 11, 34, 12, 14, 13, 36, 12, 41
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OFFSET
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1,3
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COMMENTS
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The grasshopper procedure: n positions are evenly spaced around a circle, a grasshopper hops randomly to any position, after the k-th hop, the grasshopper looks clockwise and counterclockwise k positions. If one of the positions has been visited less often then the other, it hops there; if both positions have been visited an equal number of times, it hops k steps in the clockwise position. (See Mathematics Stack Exchange link for more details.)
Either a(n) = 0 or a(n) >= A003056(n).
Conjecture: a(3^n) = A087503(n-1) + 1 for n > 0. (Checked up to 3^12.) - Peter Kagey, Nov 28 2019
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LINKS
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CROSSREFS
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KEYWORD
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nonn,walk
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AUTHOR
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STATUS
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approved
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