A306527 Squares visited by a knight moving on an open-rectangle-numbered board and moving to the lowest available unvisited square at each step.

1, 8, 11, 2, 5, 10, 7, 4, 9, 16, 3, 6, 13, 22, 35, 18, 21, 12, 15, 26, 23, 14, 25, 38, 55, 20, 17, 32, 47, 70, 31, 34, 49, 30, 19, 36, 53, 50, 69, 46, 93, 48, 29, 68, 95, 72, 33, 54, 37, 24, 27, 42, 39, 56, 77, 52, 71, 74, 97, 100, 51, 76, 101

Offset: 1

Author

Scott R. Shannon, Feb 21 2019

Keywords

• nonn
• fini
• full

Comments

The half-infinite board is numbered from square 1 as follows:

.

| | | | | | | |

--+-------+-------+-------+-------+-------+-------+-------+--

| | | | | | | |

| 25 . . .24 . . .23 . . .22 . . .21 . . .20 . . .19 |

| . | | | | | | . |

--+---.---+-------+-------+-------+-------+-------+---.---+--

| . | | | | | | . |

| 26 | 13 . . .12 . . .11 . . .10 . . . 9 | 18 |

| . | . | | | | . | . |

--+---.---+---.---+-------+-------+-------+---.---+---.---+--

| . | . | | | | . | . |

| 27 | 14 | 5 . . . 4 . . . 3 | 8 | 17 |

| . | . | . | | . | . | . |

--+---.---+---.---+---.---+-------+---.---+---.---+---.---+--

| . | . | . | | . | . | . |

| 28 | 15 | 6 | 1 | 2 | 7 | 16 |

| | | | | | | |

--+-------+-------+-------+-------+-------+-------+-------+--

.

The knight begins at square 1. This is a finite sequence: after 326 steps square 562 is reached after which all squares within one knight move have been visited.

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..326
• Scott R. Shannon, Image showing the knight path. The green dot is the starting square 1, the red dot is the end square 562. 4 Blue dots have been added around the final square to show all available positions have been visited.
• Scott R. Shannon, Simplified Java code for the sequence
• N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019)

Crossrefs

Cf. A316667, A316588.