cp's OEIS Frontend

A332980 Squares visited by a knight moving on a quadruple spiral numbered board and moving to the lowest available unvisited square at each step.

%I A332980 #12 Jul 02 2020 08:50:11
%S A332980 1,10,7,2,8,3,9,4,6,5,15,12,38,11,14,21,32,20,17,28,39,13,16,19,30,18,
%T A332980 33,44,56,37,22,34,23,35,24,36,25,52,71,29,40,59,47,66,31,42,54,77,89,
%U A332980 27,62,43,55,74,86,117,70,51,94,67,48,60,41,26,65,92,49
%N A332980 Squares visited by a knight moving on a quadruple spiral numbered board and moving to the lowest available unvisited square at each step.
%C A332980 This sequence uses a quadruple 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 A332980 The sequence is finite. After 1837 steps the square with number 1748 is visited, after which all neighboring squares have been visited.
%C A332980 The lowest unvisited square during the walk is square number 1211.
%H A332980 Scott R. Shannon, <a href="/A332980/b332980.txt">Table of n, a(n) for n = 1..1838</a>
%H A332980 Scott R. Shannon, <a href="/A332980/a332980.png"> Image showing the 1837 steps of the knights' 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. The lowest unvisited square is the yellow dot.
%e A332980 The squares are numbered using the quadruple spiral numbering shown below:
%e A332980                              |
%e A332980   --49--45--41--37--33--29  48
%e A332980                          |   |
%e A332980     26--22--18--14--10  25  44
%e A332980      |               |   |   |
%e A332980     30  11---7---3   6  21  40
%e A332980      |   |       |   |   |   |
%e A332980     34  15   4-- 1---2  17  36
%e A332980      |   |   |   |       |   |
%e A332980     38  19   8   5---9--13  32
%e A332980      |   |   |               |
%e A332980     42  23  12--16--20--24--28
%e A332980      |   |
%e A332980     46  27--31--35--39--43--47--
%e A332980      |
%Y A332980 Cf. A220098, A316667, A329022, A332837 (double spiral).
%K A332980 nonn,walk,fini,full
%O A332980 1,2
%A A332980 _Scott R. Shannon_, Mar 04 2020