A343540 Squares visited by a trapped knight on a square-spiral numbered board where the knight is shifted one square up and one square to the right after each move.

1, 10, 7, 6, 5, 4, 3, 12, 13, 8, 9, 44, 45, 42, 41, 40, 39, 18, 17, 16, 15, 14, 11, 26, 27, 28, 29, 30, 31, 34, 33, 32, 35, 62, 61, 38, 37, 64, 63, 98, 97, 96, 95, 94, 93, 56, 53, 50, 47, 114, 73, 154, 109, 108, 107, 106, 105, 104, 103, 102

Offset: 1

Author

Simon S. Gurvets, Apr 18 2021

Keywords

• nonn
• fini

Comments

The squares are numbered starting with 1 at the origin (0,0). The sequence is finite: when arriving on square number a(180) = 157, there is no free square within reach for the next move.

Shifting the knight only 1 square to the right leads to an infinite sequence. Similarly, shifting only 1 square up leads to an infinite sequence. More generally, if the knight jumps (1,n) spaces and is shifted m squares to the right, m > n leads to an infinite sequence.

Links

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