A395440 Squares visited by four 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, 3, 9, 5, 19, 6, 4, 2, 8, 15, 7, 13, 11, 18, 24, 28, 26, 35, 27, 25, 47, 38, 48, 46, 22, 63, 23, 21, 41, 34, 20, 40, 44, 17, 39, 67, 71, 62, 36, 64, 74, 33, 61, 97, 45, 30, 32, 60, 42, 53, 29, 31, 69, 84, 52, 54, 104, 49, 83, 85, 37, 78, 80, 50

Offset

1,2

Comments

All four knights, numbered 1..4, 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 1739 after visiting 477 squares, knight 3 is trapped on square 3850 after visiting 1378 squares, knight 1 is trapped on square 9876 after visiting 3982 squares, and knight 4 is trapped on square 12041 after visiting 4735 squares, giving a total of 10569 visited squares.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10569

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

Crossrefs

Cf. A338290, A395439, A395441-A395444, A316667.

Sequence in context: A095406 A337028 A050769 * A395441 A330724 A351998

Adjacent sequences: A395437 A395438 A395439 * A395441 A395442 A395443

Keyword

nonn,fini,full

Author

Scott R. Shannon, Apr 23 2026

Status

approved