OFFSET
1,2
COMMENTS
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).
LINKS
EXAMPLE
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.
PROG
(C++) // See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 28 2024
STATUS
approved