A338290 Squares visited by either 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.

1, 10, 12, 3, 9, 6, 4, 15, 7, 2, 18, 5, 35, 8, 14, 11, 29, 24, 32, 27, 55, 48, 28, 23, 13, 20, 34, 39, 17, 16, 40, 19, 21, 22, 46, 41, 25, 44, 50, 71, 79, 74, 26, 45, 47, 42, 76, 69, 43, 38, 70, 63, 105, 66, 148, 99, 65, 36, 98, 61, 37, 94, 62, 31, 33, 54, 30, 85, 53, 124, 84, 51

Offset

1,2

Comments

Board is numbered with the square spiral:

17--16--15--14--13 .

| | .

18 5---4---3 12 .

| | | | .

19 6 1---2 11 .

| | | .

20 7---8---9--10 .

| .

21--22--23--24--25--26

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...

This sequence is finite, on the 3758th move or the black knight's 1879th step, square 4242 is visited, after which white wins and the game is over.

The sequences generated by 4 knights and 8 knights also produce new sequences not yet in the OEIS.

Links

Table of n, a(n) for n=1..72.

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

Crossrefs

Cf. A338288, A338289.

Sequence in context: A316914 A350444 A342356 * A365197 A284229 A078285

Adjacent sequences: A338287 A338288 A338289 * A338291 A338292 A338293

Keyword

nonn

Author

Andrew Smith, Oct 20 2020

Status

approved