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A340327
a(n) is the X-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340328 gives Y-coordinates.
3
0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 5, 5, 6, 6, 7, 7, 6, 6, 7, 7, 6, 6, 5, 5, 4, 4, 5, 5, 6, 6, 7, 7, 6, 6, 7, 7, 8, 8, 9, 9, 8, 8, 9, 9, 10, 10, 11, 11, 10, 10, 9, 9, 8, 8, 9, 9, 8, 8, 9, 9, 10, 10, 11, 11, 10, 10, 11, 11, 12, 12, 13, 13, 12
OFFSET
0,4
COMMENTS
The curve is built by successively applying the following substitution to an initial vector (1, 0) (we have 4 copies and a horizontal unit vector):
.-.
^ |
| |
| v
.------>. .------>.
The curve visits once or twice every lattice point (x, y) such that 0 <= y <= x.
The quadratic Koch curve is built from 5 copies at each step.
EXAMPLE
The curve starts as follows:
+
|42
|
+----+
|40 41
|
+----+----+
|34 |35 |38
| |39 |
+----+ +----+
|32 33 36 37
|
+----+----+ +----+
|10 |11 |30 |27 |26
| |31 | | |
+----+ +----+----+----+
|8 9 12 |13 |24 25
| |29 |28
+----+----+ +----+----+----+
|2 |3 |6 |15 |14 |19 |22
| |7 | | |18 |23 |
+----+ +----+ +----+ +----+
0 1 4 5 16 17 20 21
- so a(0) = 0,
a(5) = a(6) = a(9) = a(10) = 3.
PROG
(PARI) See Links section.
CROSSREFS
See A332249 and A340320 for similar sequences.
Cf. A340328 (Y-coordinates).
Sequence in context: A287271 A290884 A332383 * A332249 A049113 A055093
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 04 2021
STATUS
approved