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

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

Author

Daniël Karssen, Jul 07 2018

Keywords

• nonn
• fini
• full
• look

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
• N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (January, 2019)
• Author?, Adjusting the trapped knight, Youtube video, Feb 11 2019

Crossrefs

Cf. A316328, A316667, A316334, A316335.