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A316667 Squares visited by knight moves on a spirally numbered board and moving to the lowest available unvisited square at each step. 26
1, 10, 3, 6, 9, 4, 7, 2, 5, 8, 11, 14, 29, 32, 15, 12, 27, 24, 45, 20, 23, 44, 41, 18, 35, 38, 19, 16, 33, 30, 53, 26, 47, 22, 43, 70, 21, 40, 17, 34, 13, 28, 25, 46, 75, 42, 69, 104, 37, 62, 95, 58, 55, 86, 51, 48, 77, 114, 73, 108, 151, 68, 103, 64, 67, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Board is numbered with the square spiral:

.

  17--16--15--14--13

   |               |

  18   5---4---3  12   .

   |   |       |   |

  19   6   1---2  11   .

   |   |           |

  20   7---8---9--10   .

   |

  21--22--23--24--25--26

.

This sequence is finite: At step 2016, square 2084 is visited, after which there are no unvisited squares within one knight move.

LINKS

Daniël Karssen, Table of n, a(n) for n = 1..2016

Daniël Karssen, Figure showing the first 60 steps of the sequence

Daniël Karssen, Figure showing the complete sequence

Daniël Karssen, MATLAB script to generate the complete sequence

Neil Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019)

FORMULA

a(n) = A316328(n-1) + 1.

CROSSREFS

Cf. A316588.

The (x,y) coordinates of cell k are (A174344(k), A274923(k)).

Sequence in context: A241887 A182493 A323763 * A323808 A110409 A064211

Adjacent sequences:  A316664 A316665 A316666 * A316668 A316669 A316670

KEYWORD

nonn,fini,full,look

AUTHOR

Daniël Karssen, Jul 10 2018, following a suggestion from N. J. A. Sloane, Jul 09 2018

STATUS

approved

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Last modified June 26 04:11 EDT 2019. Contains 324369 sequences. (Running on oeis4.)