A396295 - OEIS

%I #18 May 23 2026 10:32:33

%S 19,23,47,57,61,62,68,128,129,131,137,162,173,179,205,217,223,227,284,

%T 293,327,331,332,337,338,344,345,372,382,388,397,403,406,411,465,470,

%U 471,473,476,477,540,548,557,613,622,631,633,637,640,647,686,694,723,729,732,801,807,813,817,821,823,824,826,898,904,907,910,1020

%N Walk along the hexagonal spiral, with its cells numbered starting at 0, as in A395362. Two players, Black and Red, take turns. When it is Black's turn, he places a (Glinski) queen at the smallest unoccupied cell not attacked by an existing Red queen, and when it is Red's turn, she places a queen at the smallest unoccupied cell not attacked by an existing Black queen. Sequence lists cells occupied by Red queens.

%C These are Glinski queens, as in hexagonal chess (see A396292).

%C There is a subtle point about the definition. Because the players take turns placing a queen, the spiral is not filled in consecutively. To obtain the sequence, one must first fill in the whole spiral, and then return to the start, and record the Red queens that are encountered as one walks along the spiral.

%H Jonas Karlsson, <a href="/A396295/b396295.txt">Table of n, a(n) for n = 0..19999</a>

%H Jonas Karlsson, <a href="/A396295/a396295.png">The first 20000 queens in the spiral, 10000 of each color</a>

%H Jonas Karlsson, <a href="/A396295/a396295_1.png"> The first 200000 queens in the spiral</a>

%H Jonas Karlsson, <a href="/A396295/a396295_2.png">The first two million queens in the spiral</a>

%Y Cf. A395362, A395365-A395367, A396292, A396294, A396296.

%K nonn

%O 0,1

%A _Jonas Karlsson_ and _N. J. A. Sloane_, May 22 2026