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Consider the Hilbert curve with its cells numbered starting at 0. Two players take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of the other player. Sequence lists unoccupied cels.
4

%I #6 Jun 25 2026 08:32:52

%S 8,9,11,12,13,14,18,24,27,28,29,30,34,35,39,40,45,50,52,54,55,56,57,

%T 62,64,67,68,69,70,76,77,78,79,88,89,91,92,93,94,95,99,107,108,109,

%U 115,116,117,118,119,120,122,123,124,125,127,128,129,136,139,140,141

%N Consider the Hilbert curve with its cells numbered starting at 0. Two players take turns and place knights at the smallest unoccupied cell not attacked by an existing knight of the other player. Sequence lists unoccupied cels.

%H Rémy Sigrist, <a href="/A397054/b397054.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A397054/a397054.gp.txt">PARI program</a>

%o (PARI) \\ See Links section.

%Y Cf. A392177, A397052, A397053, A397055.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Jun 18 2026