A338289 Squares visited by the black 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, 12, 9, 4, 7, 18, 35, 14, 29, 32, 55, 28, 13, 34, 17, 40, 21, 46, 25, 50, 79, 26, 47, 76, 43, 70, 105, 148, 65, 98, 37, 62, 33, 30, 53, 84, 49, 52, 87, 56, 59, 92, 89, 58, 91, 130, 57, 88, 127, 174, 229, 122, 167, 82, 119, 78, 115, 160, 75, 72, 107, 150, 201, 104, 147, 144, 193, 140, 95, 136, 185, 132, 135, 184, 181

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 black knight's 1879th step, square 4242 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. A338288, A338290.

Sequence in context: A101501 A299515 A326927 * A018870 A327470 A068614

Adjacent sequences: A338286 A338287 A338288 * A338290 A338291 A338292

Keyword

nonn,fini

Author

Andrew Smith, Oct 20 2020

Status

approved