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.

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

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 * A336208 A330189 A362027

Adjacent sequences: A323805 A323806 A323807 * A323809 A323810 A323811

Keyword

nonn,walk

Author

Daniël Karssen, Jan 28 2019

Status

approved