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

1,2

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

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.

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

Status

approved