A395444 Squares visited by eight knights, all starting on square 1, when moving on a square-spiral numbered board and always moving to the lowest available unvisited square.

1, 10, 12, 14, 16, 18, 20, 22, 24, 3, 9, 5, 19, 7, 23, 41, 11, 6, 4, 2, 8, 40, 44, 68, 26, 15, 13, 25, 21, 17, 71, 37, 47, 32, 28, 46, 70, 34, 74, 62, 76, 29, 51, 75, 39, 59, 45, 33, 43, 52, 48, 42, 36, 30, 78, 58, 108, 49, 27, 69, 61, 53, 115, 55, 73, 82, 50, 38

Offset

1,2

Comments

All eight knights, numbered 1..8, start at square one, and each moves in turn to the lowest available unvisited square, starting with the lowest numbered knight.

The sequence is finite - knight 7 is trapped on square 3981 after visiting 453 squares, knight 1 is trapped on square 4118 after visiting 550 squares, knight 2 is trapped on square 8303 after visiting 1037 squares, knight 5 is trapped on square 7753 after visiting 1231 squares, knight 4 is trapped on square 7321 after visiting 1709 squares, knight 6 is trapped on square 12350 after visiting 2048 squares, knight 3 is trapped on square 7837 after visiting 2415 squares, and knight 8 is trapped on square 10319 after visiting 3799 squares, giving a total of 13235 visited squares.

All similar sequences with 9 or more knights will be identical to this one as any knight beyond the first eight will not be able to take a first step as all eight squares around the starting square will already be occupied.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..13235

Scott R. Shannon, Image of the knights' paths. The knights' paths are colored red, yellow, green, blue, indigo, violet, dark gray and light gray, the final squares for knights 1..7 are colored yellow, and the final square for knight 8 is colored red.

Crossrefs

Cf. A338290, A395439-A395443, A316667.

Sequence in context: A351998 A395442 A395443 * A088381 A163750 A356660

Adjacent sequences: A395441 A395442 A395443 * A395445 A395446 A395447

Keyword

nonn,fini,full

Author

Scott R. Shannon, Apr 23 2026

Status

approved