A329232 The number of counterclockwise steps during the grasshopper procedure.

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

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 Mathematics 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

Mathematics 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