A316588 Squares visited by knight moves on a diagonally numbered Q1 board and moving to the lowest available unvisited square at each step. Starting square is labeled 1.

1, 8, 6, 2, 12, 9, 4, 3, 13, 7, 5, 10, 26, 18, 11, 30, 24, 16, 38, 31, 22, 17, 25, 20, 28, 34, 14, 21, 43, 33, 27, 19, 15, 35, 42, 32, 23, 29, 39, 47, 56, 69, 37, 48, 40, 51, 60, 70, 57, 67, 81, 46, 58, 49, 41, 52, 44, 55, 64, 36, 65, 53, 45, 76, 63, 54, 66

Offset

1,2

Comments

Board is numbered as follows:

1 2 4 7 11 16 .

3 5 8 12 17 .

6 9 13 18 .

10 14 19 .

15 20 .

21 .

.

This sequence is finite: At step 2402, square 1378 is visited, after which there are no unvisited squares within one knight move.

Links

Daniël Karssen, Table of n, a(n) for n = 1..2402

Daniël Karssen, Figure showing the complete sequence

Daniël Karssen, MATLAB script to generate the complete sequence

Let's Code Physics, Adjusting the trapped knight, Youtube video, Feb 11 2019

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

Crossrefs

Cf. A316328, A316667, A316334, A316335.

Sequence in context: A199785 A380142 A195497 * A323810 A342946 A195336

Adjacent sequences: A316585 A316586 A316587 * A316589 A316590 A316591

Keyword

nonn,fini,full,look

Author

Daniël Karssen, Jul 07 2018

Extensions

Minor edits to definition - N. J. A. Sloane, Feb 16 2026

Status

approved