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%I #24 Mar 24 2022 16:32:25
%S 1,8,11,2,5,10,7,4,9,16,3,6,13,22,35,18,21,12,15,26,23,14,25,38,55,20,
%T 17,32,47,70,31,34,49,30,19,36,53,50,69,46,93,48,29,68,95,72,33,54,37,
%U 24,27,42,39,56,77,52,71,74,97,100,51,76,101
%N Squares visited by a knight moving on an open-rectangle-numbered board and moving to the lowest available unvisited square at each step.
%C The half-infinite board is numbered from square 1 as follows:
%C .
%C | | | | | | | |
%C --+-------+-------+-------+-------+-------+-------+-------+--
%C | | | | | | | |
%C | 25 . . .24 . . .23 . . .22 . . .21 . . .20 . . .19 |
%C | . | | | | | | . |
%C --+---.---+-------+-------+-------+-------+-------+---.---+--
%C | . | | | | | | . |
%C | 26 | 13 . . .12 . . .11 . . .10 . . . 9 | 18 |
%C | . | . | | | | . | . |
%C --+---.---+---.---+-------+-------+-------+---.---+---.---+--
%C | . | . | | | | . | . |
%C | 27 | 14 | 5 . . . 4 . . . 3 | 8 | 17 |
%C | . | . | . | | . | . | . |
%C --+---.---+---.---+---.---+-------+---.---+---.---+---.---+--
%C | . | . | . | | . | . | . |
%C | 28 | 15 | 6 | 1 | 2 | 7 | 16 |
%C | | | | | | | |
%C --+-------+-------+-------+-------+-------+-------+-------+--
%C .
%C The knight begins at square 1. This is a finite sequence: after 326 steps square 562 is reached after which all squares within one knight move have been visited.
%H Scott R. Shannon, <a href="/A306527/b306527.txt">Table of n, a(n) for n = 1..326</a>
%H Scott R. Shannon, <a href="/A306527/a306527.png">Image showing the knight path</a>. The green dot is the starting square 1, the red dot is the end square 562. 4 Blue dots have been added around the final square to show all available positions have been visited.
%H Scott R. Shannon, <a href="/A306527/a306527.java.txt">Simplified Java code for the 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)
%Y Cf. A316667, A316588.
%K nonn,fini,full
%O 1,2
%A _Scott R. Shannon_, Feb 21 2019
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