This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A346123 #16 Aug 08 2021 01:38:22 %S A346123 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 A346123 54,55,56,58,59,62 %N A346123 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 A346123 The segments of the walk can make relative turns of +- 60 degrees. The walks may be open or closed. %H A346123 Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a346123.htm">Examples of paths of maximum length</a>. %F A346123 a(n+1) >= a(n) + 1 for n > 1; a(1) = 1. %e A346123 Illustration of initial terms: %e A346123 %%% %%% %%% %e A346123 % % %e A346123 % % %e A346123 % % % /% %e A346123 % % % a(2) = 2 / % %e A346123 %__________% % / % %e A346123 % L = 1 % % / % %e A346123 % D = 1 % % L = 2, D = 1.732 / % %e A346123 % % % / % %e A346123 % / Pi/3 % %e A346123 a(1) = 1 %-------------- . . . .% %e A346123 % % %e A346123 % % %e A346123 %%% %%% %%% %e A346123 . %e A346123 %%% %%%% %%% %%% %%%% %%% %e A346123 % % % % %e A346123 % % % \ % %e A346123 % % % \ % %e A346123 % % % \ % %e A346123 % % % \ % %e A346123 % % % \ % %e A346123 %. L = 3, D = 2.00 .% %. L = 4, D = 2.00 .% %e A346123 % \ / % % \ / % %e A346123 % \ / % % \ / % %e A346123 % \ / % % \ / % %e A346123 % \ / % % \ / % %e A346123 % ---------------- % % ---------------- % %e A346123 %%% %%% %%% %%% %%% %%% %e A346123 . %e A346123 %%% %%% %%% %%% %%% %%% %e A346123 % ______________ % % ______________ % %e A346123 % \ % % / \ % %e A346123 % \ % % / \ % %e A346123 % \ % % / \ % %e A346123 % \ % % / a(3) = 6 \ % %e A346123 % \ % % / \ % %e A346123 %. L = 5, D = 2.00 .% %. L = 6, D = 2.00 .% %e A346123 % \ / % % \ / % %e A346123 % \ / % % \ / % %e A346123 % \ / % % \ / % %e A346123 % \ / % % \ / % %e A346123 % ---------------- % % ---------------- % %e A346123 %%% %%%% %%% %%% %%%% %%% %e A346123 . %e A346123 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 A346123 See link for illustrations of terms corresponding to diameters D <= 9.85. %Y A346123 Cf. A122223, A127399, A127400, A127401, A258206, A266925. %Y A346123 Cf. A346124-A346132 similar to this sequence with other sets of turning angles. %K A346123 nonn,more %O A346123 1,2 %A A346123 _Hugo Pfoertner_, Jul 05 2021