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A308884 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. 15
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
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.
LINKS
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.
EXAMPLE
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.
CROSSREFS
Sequence in context: A214211 A099384 A015716 * A101598 A342461 A157129
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 01 2019
STATUS
approved

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Last modified April 14 10:04 EDT 2024. Contains 371657 sequences. (Running on oeis4.)