cp's OEIS Frontend

A316667 Squares visited by a knight moving on a spirally numbered board always to the lowest available unvisited square.

%I A316667 #46 Jul 16 2020 18:31:16
%S A316667 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 A316667 19,16,33,30,53,26,47,22,43,70,21,40,17,34,13,28,25,46,75,42,69,104,
%U A316667 37,62,95,58,55,86,51,48,77,114,73,108,151,68,103,64,67,36
%N A316667 Squares visited by a knight moving on a spirally numbered board always to the lowest available unvisited square.
%C A316667 Board is numbered with the square spiral:
%C A316667 .
%C A316667   17--16--15--14--13   .
%C A316667    |               |   .
%C A316667   18   5---4---3  12   .
%C A316667    |   |       |   |   .
%C A316667   19   6   1---2  11   .
%C A316667    |   |           |   .
%C A316667   20   7---8---9--10   .
%C A316667    |                   .
%C A316667   21--22--23--24--25--26
%C A316667 .
%C A316667 This sequence is finite: At step 2016, square 2084 is visited, after which there are no unvisited squares within one knight move.
%H A316667 Daniël Karssen, <a href="/A316667/b316667.txt">Table of n, a(n) for n = 1..2016</a>
%H A316667 Daniël Karssen, <a href="/A316667/a316667.svg">Figure showing the first 60 steps of the sequence </a>
%H A316667 Daniël Karssen, <a href="/A316667/a316667_1.svg">Figure showing the complete sequence</a>
%H A316667 Daniël Karssen, <a href="/A316667/a316667.m.txt">MATLAB script to generate the complete sequence</a>
%H A316667 N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019)
%F A316667 a(n) = A316328(n-1) + 1.
%o A316667 (PARI) A316667(n)=A316328(n-1)+1 \\ _M. F. Hasler_, Nov 06 2019
%Y A316667 Cf. A316328 (same starting at 0), A329022 (same with diamond-shaped spiral), A316588 (variant on board with x,y >= 0).
%Y A316667 Cf. A326924 (choose square closest to the origin), A328908 (using taxicab distance), A328909 (using sup norm); A323808, A323809.
%Y A316667 The (x,y) coordinates of square k are (A174344(k), A274923(k)).
%K A316667 nonn,fini,full,look
%O A316667 1,2
%A A316667 _Daniël Karssen_, Jul 10 2018, following a suggestion from _N. J. A. Sloane_, Jul 09 2018