A395440 - OEIS

%I #9 May 18 2026 10:11:49

%S 1,10,12,14,16,3,9,5,19,6,4,2,8,15,7,13,11,18,24,28,26,35,27,25,47,38,

%T 48,46,22,63,23,21,41,34,20,40,44,17,39,67,71,62,36,64,74,33,61,97,45,

%U 30,32,60,42,53,29,31,69,84,52,54,104,49,83,85,37,78,80,50

%N Squares visited by four knights, all starting on square 1, when moving on a square-spiral numbered board and always moving to the lowest available unvisited square.

%C All four knights, numbered 1..4, start at square one, and each moves in turn to the lowest available unvisited square, starting with the lowest numbered knight.

%C The sequence is finite - knight 2 is trapped on square 1739 after visiting 477 squares, knight 3 is trapped on square 3850 after visiting 1378 squares, knight 1 is trapped on square 9876 after visiting 3982 squares, and knight 4 is trapped on square 12041 after visiting 4735 squares, giving a total of 10569 visited squares.

%H Scott R. Shannon, <a href="/A395440/b395440.txt">Table of n, a(n) for n = 1..10569</a>

%H Scott R. Shannon, <a href="/A395440/a395440_1.png">Image of the knights' paths</a>. The knights' paths are colored red, yellow, green and blue, the final squares for knights 1, 2 and 3 are colored yellow, and the final square for knight 4 is colored red.

%Y Cf. A338290, A395439, A395441-A395444, A316667.

%K nonn,fini,full

%O 1,2

%A _Scott R. Shannon_, Apr 23 2026