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A372341
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Let F be the set of lattice points {(x, y) in N^2 | A005206(x) <= y <= A005206(x) + x}; order the points of F by ascending Y-coordinates and then by ascending X-coordinates; the n-th and a(n)-th points of F are arranged symmetrically with respect to the line x = y.
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2
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1, 2, 4, 3, 5, 7, 6, 8, 11, 16, 9, 12, 17, 22, 29, 10, 13, 18, 23, 30, 37, 14, 19, 24, 31, 38, 46, 56, 15, 20, 25, 32, 39, 47, 57, 67, 21, 26, 33, 40, 48, 58, 68, 79, 92, 27, 34, 41, 49, 59, 69, 80, 93, 106, 121, 28, 35, 42, 50, 60, 70, 81, 94, 107, 122, 137
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OFFSET
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1,2
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COMMENTS
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The set F is related to the "Quilt Tiling" described in Shectman's paper (see Links section) and has interesting properties: F is symmetrical with respect to the line x = y, for any n >= 0, there are n+1 points in F with a X-coordinate of n (or with a Y-coordinate of n).
This sequence is a self-inverse permutation of the positive integers with infinitely many fixed points (see A372231).
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LINKS
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EXAMPLE
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The elements of F with coordinates <= 10 are as follows:
| +-------------------+
10 | | 56 57 58 59 60|
| | |
9 | | 46 47 48 49 50|
| +---+ |
8 | | 37| 38 39 40 41 42|
| +---+---+ |
7 | | 29 30| 31 32 33 34 35|
| | | |
6 | | 22 23| 24 25 26 27 28|
| +---+-------+-------+---+-------+
5 | | 16 17 18| 19 20| 21|
| | | +---+
4 | | 11 12 13| 14 15|
| +---+ +-------+
3 | | 7| 8 9 10|
| +---+---+---+-------+
2 | | 4 5| 6|
| | +---+
1 | | 2 3|
+---+-------+
0 | 1|
---+---+----------------------------------------
y/x| 0 1 2 3 4 5 6 7 8 9 10
So a(1) = 1, a(2) = 2, a(3) = 4, a(5) = 5, a(6) = 7, a(8) = 8, a(9) = 11, a(10) = 16, a(12) = 12, a(13) = 17, etc.
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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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nonn
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AUTHOR
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STATUS
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approved
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