A393450 - OEIS

%I #46 May 29 2026 15:22:32

%S 0,2,5,6,11,12,13,18,19,20,21,28,29,30,31,32,39,40,41,42,43,44,53,54,

%T 55,56,57,58,59,68,69,70,71,72,73,74,75,86,87,88,89,90,91,92,93,94,

%U 105,106,107,108,109,110,111,112,113,114,127,128,129,130,131,132,133,134,135,136,137,150,151,152,153,154,155,156,157,158,159

%N Consider the square spiral with its cells numbered starting at 0, as in A308884 and A274641. Two players, Black and Red, take turns. When it is Black's turn, he places a king at the smallest unoccupied cell not attacked by an existing Red king, and when it is Red's turn, she places a king at the smallest unoccupied cell not attacked by an existing Black king. Sequence lists squares occupied by a Black king.

%C Similar to A392177 and A392178, but placing kings instead of knights.

%H Jonas Karlsson, <a href="/A393450/b393450.txt">Table of n, a(n) for n = 0..19999</a> (terms 0..9999 from Michael S. Branicky)

%H Michael S. Branicky, <a href="/A393450/a393450.py.txt">Python program for OEIS A393450 and A393451</a>

%H Jonas Karlsson, <a href="/A393450/a393450.png">Illustration of first 3200 squares of the spiral</a>

%o (Python) # see linked program

%Y Cf. A393451 (Red kings). See also A308884, A274641, A392177, A392178 (knights).

%Y For kings of a single color, see A307188.

%Y For queens, see A273059, A395348, and A395349.

%K nonn

%O 0,2

%A _Jonas Karlsson_ and _N. J. A. Sloane_, Apr 20 2026