

A329232


The number of counterclockwise steps during the grasshopper procedure.


4



0, 0, 1, 0, 2, 3, 3, 0, 9, 6, 4, 5, 4, 5, 7, 0, 18, 10, 4, 7, 10, 14, 31, 15, 11, 9, 25, 16, 19, 23, 12, 0, 28, 15, 21, 29, 25, 17, 16, 38, 26, 30, 18, 26, 49, 29, 43, 29, 38, 23, 37, 31, 55, 43, 46, 53, 25, 42, 62, 51, 29, 51, 56, 0, 31, 56, 69, 22, 35, 65
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OFFSET

1,5


COMMENTS

The grasshopper procedure: n positions are evenly spaced around a circle, a grasshopper hops randomly to any position, after the kth 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 Math Stack Exchange link for more details.)
Conjecture: a(n)=0 if and only if n = 2^k.


LINKS

Peter Kagey, Table of n, a(n) for n = 1..2048
Math Stack Exchange User Vepir, Grasshopper jumping on circles


CROSSREFS

Cf. A329230, A329231, A329233.
Sequence in context: A106242 A121474 A138003 * A057682 A124841 A085355
Adjacent sequences: A329229 A329230 A329231 * A329233 A329234 A329235


KEYWORD

nonn,walk


AUTHOR

Peter Kagey, Nov 10 2019


STATUS

approved



