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A316667 Squares visited by a knight moving on a spirally numbered board always to the lowest available unvisited square. 57

%I

%S 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 19,16,33,30,53,26,47,22,43,70,21,40,17,34,13,28,25,46,75,42,69,104,

%U 37,62,95,58,55,86,51,48,77,114,73,108,151,68,103,64,67,36

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

%C Board is numbered with the square spiral:

%C .

%C 17--16--15--14--13 .

%C | | .

%C 18 5---4---3 12 .

%C | | | | .

%C 19 6 1---2 11 .

%C | | | .

%C 20 7---8---9--10 .

%C | .

%C 21--22--23--24--25--26

%C .

%C This sequence is finite: At step 2016, square 2084 is visited, after which there are no unvisited squares within one knight move.

%H Daniël Karssen, <a href="/A316667/b316667.txt">Table of n, a(n) for n = 1..2016</a>

%H Daniël Karssen, <a href="/A316667/a316667.svg">Figure showing the first 60 steps of the sequence </a>

%H Daniël Karssen, <a href="/A316667/a316667_1.svg">Figure showing the complete sequence</a>

%H Daniël Karssen, <a href="/A316667/a316667.m.txt">MATLAB script to generate the complete sequence</a>

%H N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019)

%F a(n) = A316328(n-1) + 1.

%o (PARI) A316667(n)=A316328(n-1)+1 \\ _M. F. Hasler_, Nov 06 2019

%Y Cf. A316328 (same starting at 0), A329022 (same with diamond-shaped spiral), A316588 (variant on board with x,y >= 0).

%Y Cf. A326924 (choose square closest to the origin), A323808 (using taxicab distance), A323809 (using sup norm).

%Y The (x,y) coordinates of square k are (A174344(k), A274923(k)).

%K nonn,fini,full,look

%O 1,2

%A _Daniël Karssen_, Jul 10 2018, following a suggestion from _N. J. A. Sloane_, Jul 09 2018

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Last modified May 30 08:43 EDT 2020. Contains 334712 sequences. (Running on oeis4.)