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A308884
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Follow along the squares in the square spiral (as in A274641); in each square write the smallest nonnegative number that a knight placed at that square cannot see.
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13
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0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 3, 3, 2, 0, 1, 3, 2, 1, 0, 3, 3, 3, 2, 0, 1, 3, 3, 1, 0, 0, 0, 3, 3, 0, 0, 0, 2, 1, 3, 3, 0, 0, 0, 2, 2, 3, 2, 0, 0, 0, 2, 1, 3, 3, 1, 2, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 3, 2, 1, 0, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1
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OFFSET
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0,8
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COMMENTS
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Similar to A274641, except that here we consider the mex of squares that are a knight's moves rather than queen's moves.
Since there are at most 4 earlier cells in the spiral at a knight's move from any square, a(n) <= 4.
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LINKS
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Table of n, a(n) for n=0..93.
F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, Queens in exile: non-attacking queens on infinite chess boards, Electronic J. Combin., 27:1 (2020), #P1.52.
N. J. A. Sloane, Beginning of the spiral showing the initial values.
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EXAMPLE
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A knight at square 0 cannot see any numbers, so a(0)=0. Similarly a(1)=a(2)=a(3)=0.
A knight at square 4 in the spiral can see the 0 in square 1 (because square 1 is a knight's move from square 4), so a(4) = 1. Similarly a(5)=a(6)=1.
A knight at square 7 can see a(2)=0 and a(4)=1, so a(7) = mex{0,1} = 2.
And so on. See the illustration for the start of the spiral.
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CROSSREFS
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Cf. A274641, A308885-A308895.
Sequence in context: A214211 A099384 A015716 * A101598 A157129 A101615
Adjacent sequences: A308881 A308882 A308883 * A308885 A308886 A308887
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Jul 01 2019
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STATUS
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approved
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