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%I #16 Aug 08 2021 01:38:22
%S 1,2,6,7,10,12,13,14,15,16,23,24,25,27,28,30,33,36,37,38,42,43,46,53,
%T 54,55,56,58,59,62
%N Numbers m such that no self-avoiding walk of length m + 1 on the honeycomb net fits into the smallest circle that can enclose a walk of length m.
%C The segments of the walk can make relative turns of +- 60 degrees. The walks may be open or closed.
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a346123.htm">Examples of paths of maximum length</a>.
%F a(n+1) >= a(n) + 1 for n > 1; a(1) = 1.
%e Illustration of initial terms:
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%e % %
%e % %
%e % % % /%
%e % % % a(2) = 2 / %
%e %__________% % / %
%e % L = 1 % % / %
%e % D = 1 % % L = 2, D = 1.732 / %
%e % % % / %
%e % / Pi/3 %
%e a(1) = 1 %-------------- . . . .%
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%e .
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%e %. L = 3, D = 2.00 .% %. L = 4, D = 2.00 .%
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%e % \ / % % \ / %
%e % ---------------- % % ---------------- %
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%e .
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%e % ______________ % % ______________ %
%e % \ % % / \ %
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%e % \ % % / a(3) = 6 \ %
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%e %. L = 5, D = 2.00 .% %. L = 6, D = 2.00 .%
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%e .
%e The path of minimum diameter of length 7 requires an enclosing circle of D = 3.055, which is greater than the previous minimum diameter of D = 2.00 corresponding to a(3) = 6. No path of length 8 exists that fits into a circle of D = 3.055, thus a(4) = 7.
%e See link for illustrations of terms corresponding to diameters D <= 9.85.
%Y Cf. A122223, A127399, A127400, A127401, A258206, A266925.
%Y Cf. A346124-A346132 similar to this sequence with other sets of turning angles.
%K nonn,more
%O 1,2
%A _Hugo Pfoertner_, Jul 05 2021
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