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A323808 Squares visited by a knight on a spirally numbered board and moving to the lowest available unvisited square at each step and if no unvisited squares are available move one step back. 6
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, 39, 66, 63 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is an infinite extension of A316667 with which it agrees for the first 2016 terms. - N. J. A. Sloane, Jan 28 2019

LINKS

Daniël Karssen, Table of n, a(n) for n = 1..100000

M. F. Hasler, Knight tours, OEIS wiki, Nov. 2019.

Daniël Karssen, Figure showing the first 1e5 steps of the sequence

FORMULA

a(n) = A323809(n-1) + 1. - M. F. Hasler, Nov 06 2019

EXAMPLE

The board is numbered with the square spiral:

  17--16--15--14--13   :

   |               |   :

  18   5---4---3  12  29

   |   |       |   |   |

  19   6   1---2  11  28

   |   |           |   |

  20   7---8---9--10  27

   |                   |

  21--22--23--24--25--26

See A323809 for examples where "backtracking" happens. - M. F. Hasler, Nov 06 2019

PROG

(PARI) A323808(n)=A323809(n-1)+1 \\ M. F. Hasler, Nov 06 2019

CROSSREFS

The sequences involved in this set of related sequences are A316588, A316328, A316334, A316667, A323808, A323809, A323810, and A323811.

Cf. A326924 & A326922 (using L2-norm), A328908 & A328928 (L1-norm), A328909 & A328929 (sup norm); A326916 & A326918 (digits on spiral), A326413 and A328698 (variants with other tie breaker).

Sequence in context: A316667 A329518 A329519 * A330189 A330008 A110409

Adjacent sequences:  A323805 A323806 A323807 * A323809 A323810 A323811

KEYWORD

nonn,walk

AUTHOR

Daniël Karssen, Jan 28 2019

STATUS

approved

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Last modified May 30 09:24 EDT 2020. Contains 334723 sequences. (Running on oeis4.)