A329233 The time of the first counterclockwise step during the grasshopper procedure, or 0 if no counterclockwise steps occur.

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

Offset

1,3

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.)

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

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Mathematics Stack Exchange User Vepir, Grasshopper jumping on circles

Crossrefs

Cf. A003056, A329230, A329231, A329232.

Sequence in context: A326052 A004482 A376660 * A111677 A326186 A326055

Adjacent sequences: A329230 A329231 A329232 * A329234 A329235 A329236

Keyword

nonn,walk

Author

Peter Kagey, Nov 10 2019

Status

approved