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A340172
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List of Y-coordinates of point moving along one of the arms of a counterclockwise double square spiral; A340171 gives X-coordinates.
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3
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0, 0, 1, 1, 1, 1, 0, -1, -2, -2, -2, -2, -2, -2, -1, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 0, -1, -2, -3, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -6, -6, -6
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,9
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COMMENTS
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The odd function f such that f(n) = (A340171(n), a(n)) for any n >= 0 will visit exactly once every lattice point (so it is a bijection from Z to Z^2).
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LINKS
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FORMULA
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EXAMPLE
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The spiral starts as follows:
+-----+-----+-----+-----+-----+
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. +-----+-----+-----+ +
. |5 4 3 |2 |
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+ +-----+-----+ +
|6 | 0 1 | .
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+ +-----+-----+-----+ .
|7 .
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+-----+-----+-----+-----+-----+
8 9 10 11 12 13
- so a(0) = a(1) = a(6) = 0,
- a(2) = a(3) = a(4) = a(5) = 1.
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PROG
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(PARI) See Links section.
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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