A338288 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.

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, 38, 6, 66, 99, 36, 61, 94, 31, 54, 85, 124, 51, 80, 83, 120, 123, 168, 81, 118, 77, 114, 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

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 white knight's 3999th step, square 3606 is visited, after which there are no unvisited squares within one knight move.

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..75.

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

Crossrefs

Cf. A338289, A338290.

Sequence in context: A362027 A358150 A335214 * A330008 A335844 A110409

Adjacent sequences: A338285 A338286 A338287 * A338289 A338290 A338291

Keyword

nonn,fini

Author

Andrew Smith, Oct 20 2020

Status

approved