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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.
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%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