A349196 a(n) is the Y-coordinate of the n-th point of the R5 dragon curve; A349195 gives X-coordinates.

0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 3, 3, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, -1, -1, -2, -2, -1, -1, -2, -2, -1, -1, 0, 0, -1, -1, 0, 0, -1, -1, -2, -2, -3, -3, -2, -2, -3, -3

Offset

0,5

Comments

The R5 dragon curve can be represented using an L-system.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..3125

Kevin Ryde, Iterations of the R5 Dragon Curve

Rémy Sigrist, Colored representation of the first 1 + 5^9 points of the R5 dragon curve (where the hue is function of the number of steps from the origin)

Rémy Sigrist, PARI program for A349196

Index entries for sequences related to coordinates of 2D curves

Formula

a(5^k) = A006496(k) for any k >= 0.

Example

The R5 dragon curve starts as follows:
         +-----+
       24|   25
         |
         |
         +-----+     +-----+     +-----+
       23    22|   11|   10|    7|    6|
               |     |     |     |     |
             21|   12|    9|    8|     |
         +-----+-----+-----+-----+-----+
       20|   17|   16|   13|    4|    5
         |     |     |     |     |
         |     |     |     |     |
         +-----+     +-----+     +-----+
       19    18    15    14     3     2|
                                       |
                                       |
                                 +-----+
                                0     1
- so a(0) = a(1) = 0,
     a(2) = a(3) = a(14) = a(15) = a(18) = a(19) = 1.

Prog

(PARI) See Links section.

Crossrefs

Cf. A006496, A349008, A349009, A349010, A349195.

Sequence in context: A367007 A130326 A059906 * A112046 A076902 A287271

Adjacent sequences: A349193 A349194 A349195 * A349197 A349198 A349199

Keyword

sign

Author

Rémy Sigrist, Nov 10 2021

Status

approved