cp's OEIS Frontend

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.

%I A323808 #17 Nov 06 2019 23:54:14
%S A323808 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,
%T A323808 19,16,33,30,53,26,47,22,43,70,21,40,17,34,13,28,25,46,75,42,69,104,
%U A323808 37,62,95,58,55,86,51,48,77,114,73,108,151,68,103,64,67,36,39,66,63
%N 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.
%C A323808 This is an infinite extension of A316667 with which it agrees for the first 2016 terms. - _N. J. A. Sloane_, Jan 28 2019
%H A323808 Daniël Karssen, <a href="/A323808/b323808.txt">Table of n, a(n) for n = 1..100000</a>
%H A323808 M. F. Hasler, <a href="/wiki/Knight_tours">Knight tours</a>, OEIS wiki, Nov. 2019.
%H A323808 Daniël Karssen, <a href="/A323808/a323808.svg">Figure showing the first 1e5 steps of the sequence</a>
%F A323808 a(n) = A323809(n-1) + 1. - _M. F. Hasler_, Nov 06 2019
%e A323808 The board is numbered with the square spiral:
%e A323808   17--16--15--14--13   :
%e A323808    |               |   :
%e A323808   18   5---4---3  12  29
%e A323808    |   |       |   |   |
%e A323808   19   6   1---2  11  28
%e A323808    |   |           |   |
%e A323808   20   7---8---9--10  27
%e A323808    |                   |
%e A323808   21--22--23--24--25--26
%e A323808 See A323809 for examples where "backtracking" happens. - _M. F. Hasler_, Nov 06 2019
%o A323808 (PARI) A323808(n)=A323809(n-1)+1 \\ _M. F. Hasler_, Nov 06 2019
%Y A323808 The sequences involved in this set of related sequences are A316588, A316328, A316334, A316667, A323808, A323809, A323810, and A323811.
%Y A323808 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).
%K A323808 nonn,walk
%O A323808 1,2
%A A323808 _Daniël Karssen_, Jan 28 2019