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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
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
Mathematics Stack Exchange User Vepir, Grasshopper jumping on circles
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Peter Kagey, Nov 10 2019
STATUS
approved