A340320 - OEIS

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.

%I #13 Jan 07 2021 10:31:17

%S 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,

%T 10,11,11,12,12,13,13,12,12,11,11,10,10,9,9,10,10,9,9,10,10,11,11,12,

%U 12,13,13,12,12,13,13,14,14,15,15,14,14,15,15,16,16

%N a(n) is the X-coordinate of the n-th point of a variant of the quadratic Koch curve. Sequence A340321 gives Y-coordinates.

%C The curve is built by successively applying the following substitution to an initial vector (1, 0) (the two vertical copies are horizontally flipped):

%C *

%C .------>.

%C ^ |

%C |* *|

%C * | v *

%C .------>. .------>.

%C The quadratic Koch curve is built without horizontal flip.

%H Rémy Sigrist, <a href="/A340320/b340320.txt">Table of n, a(n) for n = 0..3125</a>

%H Robert Ferréol (MathCurve), <a href="https://www.mathcurve.com/fractals/kochquadratique/kochquadratique.shtml">Courbe de Koch quadratique</a> [in French]

%H Rémy Sigrist, <a href="/A340320/a340320.png">Line plot of the first 1+5^5 points</a>

%H Rémy Sigrist, <a href="/A340320/a340320.gp.txt">PARI program for A340320</a>

%H <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>

%e The curve starts as follows:

%e +---+

%e |12 |13

%e | |

%e +---+ +---+

%e |10 11 14 |15

%e | |

%e +---+ +---+

%e 9 |8 |17 16

%e | |

%e +---+ +---+ +---+ +---+

%e |2 |3 |6 7 18 |19 |22 |23

%e | | | | | |

%e +---+ +---+ +---+ +---+

%e 0 1 4 5 20 21 24 25

%e - so a(0) = 0,

%e a(5) = a(6) = a(9) = a(10) = 3.

%o (PARI) See Links section.

%Y See A332249 and A340327 for similar sequences.

%Y Cf. A340321 (Y-coordinates).

%K nonn

%O 0,4

%A _Rémy Sigrist_, Jan 04 2021