A333684 - OEIS

%I #8 Apr 09 2020 22:19:54

%S 72085,706243,270402,236090,716518,716518,730674,657313,236090,236090,

%T 1318101,1634797,482448,901595,237177,1946730,21429,726318,706243,

%U 730674,793200,237177,405933,3095967,51035,159266,218715,106443,101767,927137,148315,786512,1495770

%N The cell number where a knight is trapped when moving on a spirally numbered hexagonal board to the lowest available unvisited cell and starting at cell n.

%C For a knight moving on a spirally numbered hexagonal board to the lowest available unvisited cell, see A327131, a(n) gives the cell number where the knight is trapped when the knight starts on the cell numbered n.

%C See A327131 for the allowed knight moves, a diagram of the hexagonal board, and an illustration of the knight's path for n = 1.

%C For the first 100000 terms the largest cell number where the knight is trapped is for starting starting cell 81479 where the final cell has number 8085793, being reached after 8125572 steps. In the same range the smallest cell number where the night is trapped is for starting cell 1036 where the final cell has number 1267, being reached after 1603 steps. See A333683 for an image of this path.

%H N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019).

%e The knight starting on cell 1 becomes trapped on cell 72085 after 83965 steps, see A327131.

%Y Cf. A333683 (number of steps), A327131, A309918, A328894, A306291.

%K nonn

%O 1,1

%A _Scott R. Shannon_, Apr 02 2020