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A361486
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Lexicographically earliest sequence of positive numbers on a square spiral such that no three equal numbers are collinear.
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3
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1, 1, 1, 1, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 3, 1, 3, 3, 1, 4, 1, 4, 3, 5, 5, 1, 4, 3, 4, 5, 4, 4, 5, 6, 6, 7, 4, 4, 5, 5, 6, 2, 4, 1, 4, 5, 1, 6, 2, 6, 4, 6, 5, 5, 7, 2, 3, 4, 6, 5, 5, 7, 2, 3, 8, 1, 4, 3, 6, 7, 5, 5, 3, 5, 7, 6, 3, 1, 1, 7, 8, 7, 7, 4, 5, 8, 5, 9, 6, 6, 8, 7, 7, 6, 8, 9, 9, 3
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OFFSET
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1,5
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COMMENTS
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The first term a(1) = 1 lies at the (0,0) origin while all other terms lie on integer coordinates.
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LINKS
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EXAMPLE
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a(5) = 2 as a(3) = 1 and a(4) = 1 lie on the horizontal line y = 1 relative to the starting square (assuming a counter-clockwise spiral) so a(5) cannot be 1.
a(7) = 3 as a(5) = 2 and a(6) = 2 lie on the vertical line x = -1 so a(7) cannot be 2, while a(1) = 1 and a(3) = 1 lie on the line y = x so a(7) cannot be 1.
a(21) = 4 as a(18) = 3 and a(19) = 3 lie on the line x = -2, a(6) = 2 and a(15) = 2 lie on the line y = 2*x + 2, while a(1) = 1 and a(3) = 1 lie on the line y = x, so a(21) cannot be 1, 2 or 3.
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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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