A323714 Squares where knight moving to a lowest unvisited square on a spirally numbered board will have no available moves.

2084, 2720, 3325, 3753, 7776, 5632, 7411, 8562, 14076, 8469, 9231, 22702, 14661, 21710, 21078, 25809, 27112, 24708, 19844, 26943, 26737, 32449, 31366, 45036, 37853, 37188, 43318, 62095, 67401, 68736

Offset: 1

Author

Sami Mäki, Jan 25 2019

Keywords

• nonn
• look

Comments

First term is the last term of A316667. Next terms are given by repeatedly blocking the squares where the knight would not have any available moves.

Plotting the terms on XY-plane seems to show a clear pattern where most of the points only land on certain directions from the center.

Inspired by A316667 and comments on N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

Links

• Sami Mäki, Table of n, a(n) for n = 1..4000
• N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019).

Crossrefs

Cf. A316667, A323808.