A396616 - OEIS

A396616

Consider the spiral of numbers in the upper half-plane with its cells numbered as in A396617, but starting at 0. Two players, Black and Red, take turns. When it is Black's turn, he places a knight at the smallest unoccupied cell not attacked by an existing Red knight, and when it is Red's turn, she places a knight at the smallest unoccupied cell not attacked by an existing Black knight. Sequence lists squares occupied by a Red knight.

%I #10 Jun 06 2026 09:34:46

%S 1,3,4,6,12,16,23,25,27,32,36,39,45,50,52,65,66,67,71,73,77,82,88,90,

%T 92,96,98,99,112,117,118,119,120,121,122,123,140,142,144,146,148,153,

%U 154,158,159,161,164,166,175,179,181,185,186,187,188,189,190,191,192,193

%N Consider the spiral of numbers in the upper half-plane with its cells numbered as in A396617, but starting at 0. Two players, Black and Red, take turns. When it is Black's turn, he places a knight at the smallest unoccupied cell not attacked by an existing Red knight, and when it is Red's turn, she places a knight at the smallest unoccupied cell not attacked by an existing Black knight. Sequence lists squares occupied by a Red knight.

%C Note that spiral is not filled in consecutively so, to obtain the sequence, one must fill in the whole spiral and then return to the start and record the Red knights that are encountered as one walks along the spiral.

%C See A396615 for images of the spiral.

%H Scott R. Shannon, <a href="/A396616/b396616.txt">Table of n, a(n) for n = 0..10000</a>

%Y Cf. A396617, A396615 (the Black knights), A392177, A392178, A392182, A392183.

%K nonn

%O 0,2

%A _Scott R. Shannon_, May 31 2026