The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A316667 Squares visited by a knight moving on a spirally numbered board always to the lowest available unvisited square. 68
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Board is numbered with the square spiral: .   17--16--15--14--13   .    |               |   .   18   5---4---3  12   .    |   |       |   |   .   19   6   1---2  11   .    |   |           |   .   20   7---8---9--10   .    |                   .   21--22--23--24--25--26 . This sequence is finite: At step 2016, square 2084 is visited, after which there are no unvisited squares within one knight move. LINKS Daniël Karssen, Table of n, a(n) for n = 1..2016 Daniël Karssen, Figure showing the first 60 steps of the sequence Daniël Karssen, Figure showing the complete sequence Daniël Karssen, MATLAB script to generate the complete sequence N. J. A. Sloane and Brady Haran, The Trapped Knight, Numberphile video (2019) FORMULA a(n) = A316328(n-1) + 1. PROG (PARI) A316667(n)=A316328(n-1)+1 \\ M. F. Hasler, Nov 06 2019 CROSSREFS Cf. A316328 (same starting at 0), A329022 (same with diamond-shaped spiral), A316588 (variant on board with x,y >= 0). Cf. A326924 (choose square closest to the origin), A328908 (using taxicab distance), A328909 (using sup norm); A323808, A323809. The (x,y) coordinates of square k are (A174344(k), A274923(k)). Sequence in context: A241887 A182493 A323763 * A329518 A329519 A323808 Adjacent sequences:  A316664 A316665 A316666 * A316668 A316669 A316670 KEYWORD nonn,fini,full,look AUTHOR Daniël Karssen, Jul 10 2018, following a suggestion from N. J. A. Sloane, Jul 09 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 26 04:11 EST 2021. Contains 340429 sequences. (Running on oeis4.)