Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #23 Oct 24 2020 07:04:55
%S 1,10,3,6,15,2,5,8,11,24,27,48,23,20,39,16,19,22,41,44,71,74,45,42,69,
%T 38,6,66,99,36,61,94,31,54,85,124,51,80,83,120,123,168,81,118,77,114,
%U 73,108,151,68,103,64,67,102,143,146,195,100,141,96,137,60,93,90,129,86,125,172,121,166,117,162,113,110,153
%N Squares visited by the white knight when a white knight and a black knight are moving on a spirally numbered board, always to the lowest available unvisited square; white moves first.
%C Board is numbered with the square spiral:
%C 17--16--15--14--13 .
%C | | .
%C 18 5---4---3 12 .
%C | | | | .
%C 19 6 1---2 11 .
%C | | | .
%C 20 7---8---9--10 .
%C | .
%C 21--22--23--24--25--26
%C Both knights start on square 1, white moves to the lowest unvisited square (10), black then moves to the lowest unvisited square (12) and so on...
%C This sequence is finite, on the white knight's 3999th step, square 3606 is visited, after which there are no unvisited squares within one knight move.
%C The sequences generated by 4 knights and 8 knights also produce new sequences not yet in the OEIS.
%H N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019).
%Y Cf. A338289, A338290.
%K nonn,fini
%O 1,2
%A _Andrew Smith_, Oct 20 2020