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A366353
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a(0) = 0; for n > 0, a(n) is the largest taxicab distance on a square spiral between a(n-1) and any previous occurrence of a(n-1). If a(n-1) has not previously occurred then a(n) = 0.
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4
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0, 0, 1, 0, 2, 0, 2, 2, 3, 0, 4, 0, 4, 2, 5, 0, 6, 0, 6, 2, 6, 4, 7, 0, 6, 8, 0, 7, 5, 4, 8, 5, 3, 4, 6, 8, 10, 0, 9, 0, 7, 7, 8, 12, 0, 7, 6, 8, 10, 12, 6, 10, 11, 0, 9, 8, 13, 0, 11, 6, 9, 6, 11, 10, 13, 8, 12, 13, 11, 10, 9, 12, 8, 15, 0, 13, 13, 12, 11, 12, 13, 16, 0, 13, 15, 11, 11, 10, 12
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OFFSET
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0,5
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LINKS
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EXAMPLE
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The spiral begins:
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10--8---6---4---3---5---8 :
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0 6---0---5---2---4 4 9
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9 0 2---0---1 0 5 0
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0 6 0 0---0 4 7 11
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7 2 2---2---3---0 0 10
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7 6---4---7---0---6---8 6
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8---12--0---7---6---8---10--12
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a(2) = 1 as the taxicab distance between a(1) = 0, at (1,0) relative to the starting square, and the only previous occurrence of 0, a(0) at (0,0), is 1.
a(8) = 3 as the maximum taxicab distance between a(7) = 2, at (0,-1) relative to the starting square, and any previous occurrence of 2 is 3, to a(4) = 2 at (-1,1) relative to the starting square.
a(32) = 3 as the maximum taxicab distance between a(31) = 5, at (2,3) relative to the starting square, and any previous occurrence of 5 is 3, to a(28) = 5 at (3,1) relative to the starting square, and also to a(14) = 5 at (0,2) relative to the starting square. This is the first term to differ from A366354.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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