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Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/4, +-Pi/2, +-3*Pi/4, of length m + 1 fits into the smallest circle that can enclose a walk of length m.
1

%I #6 Aug 03 2021 02:43:34

%S 1,2,4,5,7,8,9,11,12,13,15,17,18,19,20,22,23,24,25,26,27,28,30,31,32,

%T 33,34,35,36,37,38

%N Numbers m such that no self-avoiding walk that can make turns from the set 0, +-Pi/4, +-Pi/2, +-3*Pi/4, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

%C Closed walks (see A316198) are allowed, but except for the closed square-shaped walk of length 4 that fits into the same smallest enclosing circle as the smallest open walk of this length, no other closed walk that fits into a smaller enclosing circle than any open walk of the same length is known.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a346128.htm">Examples of paths of maximum length</a>.

%e See link for illustrations of terms corresponding to diameters D < 3.83.

%Y Cf. A127399, A127400, A127401, A306178, A316198.

%Y Cf. A346123-A346132 similar to this sequence with other sets of turning angles.

%K nonn,walk,more

%O 1,2

%A _Hugo Pfoertner_ and _Markus Sigg_, Aug 01 2021