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%I #21 Aug 12 2022 09:23:58
%S 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,
%T 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,
%U 12,16,30,11,32,17,11,0,11,11,34,12,14,13,36,12,41
%N The time of the first counterclockwise step during the grasshopper procedure, or 0 if no counterclockwise steps occur.
%C 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.)
%C Either a(n) = 0 or a(n) >= A003056(n).
%C Conjecture: a(3^n) = A087503(n-1) + 1 for n > 0. (Checked up to 3^12.) - _Peter Kagey_, Nov 28 2019
%H Peter Kagey, <a href="/A329233/b329233.txt">Table of n, a(n) for n = 1..10000</a>
%H Mathematics Stack Exchange User Vepir, <a href="https://math.stackexchange.com/q/3418970/121988">Grasshopper jumping on circles</a>
%Y Cf. A003056, A329230, A329231, A329232.
%K nonn,walk
%O 1,3
%A _Peter Kagey_, Nov 10 2019
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