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

Author

Daniël Karssen, Jan 28 2019

Keywords

• nonn
• walk

Comments

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

Examples

			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
		

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

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).

Programs

PARI

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

Formula

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