A333684 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.

72085, 706243, 270402, 236090, 716518, 716518, 730674, 657313, 236090, 236090, 1318101, 1634797, 482448, 901595, 237177, 1946730, 21429, 726318, 706243, 730674, 793200, 237177, 405933, 3095967, 51035, 159266, 218715, 106443, 101767, 927137, 148315, 786512, 1495770

Offset

1,1

Comments

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.

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

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.

Links

Table of n, a(n) for n=1..33.

N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

Example

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

Crossrefs

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

Sequence in context: A080477 A376469 A234330 * A187137 A185842 A251348

Adjacent sequences: A333681 A333682 A333683 * A333685 A333686 A333687

Keyword

nonn

Author

Scott R. Shannon, Apr 02 2020

Status

approved