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

1,2

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

Table of n, a(n) for n=1..60.

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

Crossrefs

Sequence in context: A246662 A246651 A089245 * A343551 A098592 A016731

Adjacent sequences: A343537 A343538 A343539 * A343541 A343542 A343543

Keyword

nonn,fini

Author

Simon S. Gurvets, Apr 18 2021

Status

approved