A346129 - OEIS

A346129

Numbers m such that no self-avoiding walk that can make turns from the set +-Pi/9, +-Pi/3, +-5*Pi/9, +-7*Pi/9, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

%I #5 Aug 03 2021 02:43:43

%S 1,2,4,5,6,8,9,11,12,13,14,16,17,18,19,20,21,23,24,25,26,27,28,30,31,

%T 32,33,34,35,36,37,38,39,41

%N Numbers m such that no self-avoiding walk that can make turns from the set +-Pi/9, +-Pi/3, +-5*Pi/9, +-7*Pi/9, of length m + 1 fits into the smallest circle that can enclose a walk of length m.

%C Although closed walks (see A316199) would be allowed, no 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/a346129.htm">Examples of paths of maximum length</a>.

%e See link for illustrations of terms corresponding to diameters D < 3.50.

%Y Cf. A127399, A127400, A127401, A306179, A316199.

%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