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A334576
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a(n) is the X-coordinate of the n-th point of the space filling curve P defined in Comments section; sequence A334577 gives Y-coordinates.
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2
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0, 1, 2, 2, 2, 3, 3, 3, 4, 5, 6, 6, 5, 4, 4, 4, 4, 5, 6, 6, 6, 7, 7, 7, 7, 6, 5, 5, 6, 7, 7, 7, 8, 9, 10, 10, 10, 11, 11, 11, 12, 13, 14, 14, 13, 12, 12, 12, 11, 10, 9, 9, 9, 8, 8, 8, 8, 9, 10, 10, 9, 8, 8, 8, 8, 9, 10, 10, 10, 11, 11, 11, 12, 13, 14, 14, 13
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OFFSET
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0,3
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COMMENTS
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The space filling curve P corresponds to the midpoint curve of the alternate paperfolding curve and can be built as follows:
- we define the family {P_k, k > 0}:
- P_1 corresponds to the points (0, 0), (1, 0), (2, 0) and (2, 1), in that order:
+
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+----+----+
O
- for any k > 0, P_{n+1} is built from four copies of P_n as follows:
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|A
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C| +----+ |
A B| ---> |C B| |B C
+-------+ + | +----+-+
O C| | C|
A B| A| A B|
+-------+ +-+-------+
O
- the space filling curve P is the limit of P_k as k tends to infinity.
We can also describe the space filling curve P by mean of an L-system (see Links section).
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LINKS
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FORMULA
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EXAMPLE
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The first points of the space filling curve P are as follows:
6| 20...21
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5| 19 22
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4| 16...17...18 23
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3| 15 26...25...24
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2| 4....5 14 27...28...29
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1| 3 6 13...12...11 30
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0| 0....1....2 7....8....9....10 31..
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---+----------------------------------------
y/x| 0 1 2 3 4 5 6 7
- hence a(9) = a(12) = a(17) = a(26) = a(27) = 5.
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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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nonn
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AUTHOR
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STATUS
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approved
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