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A329022 Squares visited by a knight moving on a diagonal spiral numbered board and moving to the lowest available unvisited square at each step.

%I A329022 #13 Jul 02 2020 08:49:17
%S A329022 1,14,7,3,6,4,8,5,10,2,9,17,28,43,13,15,26,24,11,20,32,48,29,44,63,25,
%T A329022 12,21,34,18,30,45,27,16,31,19,35,22,39,57,36,23,37,54,75,51,71,95,68,
%U A329022 91,65,46,69,49,33,53,74,50,70,47,66,89,116,42,40,58,80,55,38,56,77,102,131,52,72,96,124
%N A329022 Squares visited by a knight moving on a diagonal spiral numbered board and moving to the lowest available unvisited square at each step.
%C A329022 This sequence uses a diagonal spiral of numbers to enumerate the squares on the board. The knight starts on the square with number 1. At each step the knight goes to an unvisited square with the smallest number.
%C A329022 The sequence if finite. After 3722 steps the square with number 3541 is visited, after which all neighboring squares have been visited.
%H A329022 Scott R. Shannon, <a href="/A329022/b329022.txt">Table of n, a(n) for n = 1..3723</a>
%H A329022 Scott R. Shannon, <a href="/A329022/a329022.png">Image showing the 3722 steps of the knight's path</a>. The green dot is the starting square and the red dot the final square. Blue dots show the eight occupied squares surrounding the final square.
%H A329022 N. J. A. Sloane and Brady Haran, <a href="https://www.youtube.com/watch?v=RGQe8waGJ4w">The Trapped Knight</a>, Numberphile video (2019).
%e A329022 The board is numbered in a spiral moving along the diagonals of the square grid:
%e A329022 .
%e A329022                        19
%e A329022                      /   \
%e A329022                    /       \
%e A329022                  20    9     18
%e A329022                /     /   \     \
%e A329022              /     /       \     \
%e A329022            21    10    3     8     17
%e A329022          /     /     /   \     \     \
%e A329022        /     /     /       \     \     \
%e A329022      22    11    4     1 --- 2     7     16
%e A329022        \     \     \             /     /     .
%e A329022          \     \     \         /     /     .
%e A329022            23    12    5 --- 6     15    28
%e A329022              \     \             /     /
%e A329022                \     \         /     /
%e A329022                  24    13 -- 14    27
%e A329022                    \             /
%e A329022                      \         /
%e A329022                        25 -- 26
%e A329022 .
%e A329022     +----+----+----+----+----+----+----+
%e A329022     | 76 | 53 | 34 | 19 | 32 | 49 | 70 |
%e A329022     +----+----+----+----+----+----+----+
%e A329022     | 54 | 35 | 20 |  9 | 18 | 31 | 48 |
%e A329022     +----+----+----+----+----+----+----+
%e A329022     | 36 | 21 | 10 |  3 |  8 | 17 | 30 |
%e A329022     +----+----+----+----+----+----+----+
%e A329022     | 22 | 11 |  4 |  1 |  2 |  7 | 16 |
%e A329022     +----+----+----+----+----+----+----+
%e A329022     | 38 | 23 | 12 |  5 |  6 | 15 | 28 |
%e A329022     +----+----+----+----+----+----+----+
%e A329022     | 58 | 39 | 24 | 13 | 14 | 27 | 44 |
%e A329022     +----+----+----+----+----+----+----+
%e A329022     | 82 | 59 | 40 | 25 | 26 | 43 | 64 |
%e A329022     +----+----+----+----+----+----+----+
%e A329022 .
%Y A329022 Cf. A316667.
%Y A329022 Cf. A010751(n), A305258(n) for coordinates of point number n+1.
%K A329022 nonn,fini,full,walk
%O A329022 1,2
%A A329022 _Scott R. Shannon_, Nov 02 2019