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A340320 a(n) is the X-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340321 gives Y-coordinates. 3
0, 1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 4, 4, 5, 5, 6, 6, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 12, 12, 11, 11, 10, 10, 9, 9, 10, 10, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 12, 12, 13, 13, 14, 14, 15, 15, 14, 14, 15, 15, 16, 16 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
The curve is built by successively applying the following substitution to an initial vector (1, 0) (the two vertical copies are horizontally flipped):
*
.------>.
^ |
|* *|
* | v *
.------>. .------>.
The quadratic Koch curve is built without horizontal flip.
LINKS
Robert Ferréol (MathCurve), Courbe de Koch quadratique [in French]
EXAMPLE
The curve starts as follows:
+---+
|12 |13
| |
+---+ +---+
|10 11 14 |15
| |
+---+ +---+
9 |8 |17 16
| |
+---+ +---+ +---+ +---+
|2 |3 |6 7 18 |19 |22 |23
| | | | | |
+---+ +---+ +---+ +---+
0 1 4 5 20 21 24 25
- so a(0) = 0,
a(5) = a(6) = a(9) = a(10) = 3.
PROG
(PARI) See Links section.
CROSSREFS
See A332249 and A340327 for similar sequences.
Cf. A340321 (Y-coordinates).
Sequence in context: A357839 A332250 A340321 * A059998 A361384 A339731
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jan 04 2021
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)