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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

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 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

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Last modified June 16 21:55 EDT 2021. Contains 345080 sequences. (Running on oeis4.)