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A292469
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Let P be the sequence of distinct lattice points defined by the following rules: P(1) = (0,0), P(2) = (1,0), and for any n > 2, P(n) is the closest lattice point to P(n-1) such that the Z-coordinate of the cross product of the vectors (P(n-1), P(n)) and (P(n-1), P(j)) is strictly negative for j=1..n-2, and in case of a tie, P(n) maximizes the dot product of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)); a(n) = X-coordinate of P(n).
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3
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0, 1, 1, 0, -1, -1, 0, 2, 2, 1, 0, -1, -2, -2, -1, 1, 4, 4, 3, 2, -1, -2, -3, -3, -2, -1, 1, 4, 5, 5, 4, 2, 1, -1, -2, -3, -4, -4, -3, 0, 2, 5, 6, 6, 5, 3, 0, -1, -2, -3, -4, -5, -5, -4, -2, 1, 8, 8, 7, 5, 2, 1, -2, -3, -4, -5, -6, -6, -5, -4, -2, 1, 5, 10, 10
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OFFSET
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1,8
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COMMENTS
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More informally:
- the "scalar product" constraint means that the points P(1), ..., P(n-2) are all on the left side of the fixed vector (P(n-1), P(n)),
- the "dot product" constraint means the angle of the vectors (P(n-2), P(n-1)) and (P(n-1), P(n)) is maximized.
See A292470 for the Y-coordinate of P(n).
The points of sequence P spin around the origin, and the segments joining consecutive points of P do not intersect (except at the common endpoint of two consecutive segments); these properties are the original motivations for this sequence.
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LINKS
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EXAMPLE
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See representation of the first hundred points of P in Links section.
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PROG
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(C++) See Links section.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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