A395441 Squares visited by five 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, 3, 9, 5, 19, 7, 6, 4, 2, 8, 24, 15, 11, 13, 21, 27, 32, 26, 28, 40, 48, 29, 47, 25, 17, 23, 52, 22, 46, 34, 20, 49, 41, 75, 59, 39, 78, 44, 42, 30, 36, 45, 71, 69, 33, 61, 74, 106, 38, 58, 94, 109, 67, 35, 55, 31, 70, 64, 60, 86, 54, 43, 97

Offset

1,2

Comments

All five knights, numbered 1..5, 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 2 is trapped on square 2768 after visiting 570 squares, knight 3 is trapped on square 4129 after visiting 809 squares, knight 5 is trapped on square 3799 after visiting 1155 squares, knight 1 is trapped on square 5876 after visiting 1268 squares, and knight 4 is trapped on square 10535 after visiting 6209 squares, giving a total of 10007 visited squares.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10007

Scott R. Shannon, Image of the knights' paths. The knights' paths are colored red, yellow, green, blue and indigo, the final squares for knights 1, 2, 3 and 5 are colored yellow, and the final square for knight 4 is colored red.

Crossrefs

Cf. A338290, A395439, A395440, A395442-A395444, A316667.

Sequence in context: A337028 A050769 A395440 * A330724 A351998 A395442

Adjacent sequences: A395438 A395439 A395440 * A395442 A395443 A395444

Keyword

nonn,fini,full

Author

Scott R. Shannon, Apr 23 2026

Status

approved