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The minimal number of steps that a path-avoiding snail must take in order to have a step of length (2n-1)/2^k for some k.
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%I #19 Aug 12 2022 09:18:25

%S 1,7,9,8,10,11,10,9,11,12,11,12,11,12,11,10,12,13,14,13,13,14,12,13,

%T 12,13,14,13,12,13,12,11,13,14,15,14,15,14,15,14,14,15,15,14,14,14,13,

%U 14,13,14,15,14,13,15,15,14,13,14,15,14,13,14,13,12,14,15

%N The minimal number of steps that a path-avoiding snail must take in order to have a step of length (2n-1)/2^k for some k.

%C The path-avoiding snail takes steps of unit length if doing so does not cause it to collide with its trail. If a unit length step would cause a collision, it travels halfway to its trail. After every step the snail may turn left or right or remain straight.

%H Peter Kagey, <a href="https://math.stackexchange.com/q/2678852/121988">Number of steps the path-avoiding snail must take before a step size of (2n-1)/2^k?</a>, Mathematics Stack Exchange.

%K nonn,walk

%O 1,2

%A _Peter Kagey_, Mar 05 2018