A334485 a(n) is the X-coordinate of the n-th point of Gosper's flowsnake curve; sequence A334486 gives Y-coordinates.

0, 1, 1, 0, -1, 0, 1, 2, 3, 3, 3, 2, 2, 1, 1, 0, -1, -2, -1, 0, 0, -1, -2, -3, -2, -2, -3, -4, -4, -3, -3, -4, -5, -4, -3, -2, -1, -1, -2, -3, -2, -1, 0, 0, 1, 2, 2, 1, 2, 3, 4, 4, 3, 2, 3, 4, 5, 6, 6, 6, 5, 5, 4, 4, 5, 5, 5, 4, 4, 3, 3, 2, 1, 0, 1, 2, 2, 1, 1

Offset

0,8

Comments

Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:

Y

/

/

0 ---- X

The Gosper curve can be represented using an L-system.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..2401

Rémy Sigrist, Colored scatterplot of the first 7^7+1 points of the Gosper curve (where the hue is function of the number of steps from the origin; the origin is located on the right side, at the black mark)

Rémy Sigrist, PARI program for A334485

Wikipedia, Gosper curve

Index entries for sequences related to coordinates of 2D curves

Example

The Gosper curve starts (on a hexagonal lattice) as follows:
     .   .   .   .   .   +---+---+   .   .   .   .
                          \       \
       .   .   +---+---+   +---+   +   .   .   .   .
                \       \     /   /
     .   .   .   +---+   +---+   +   +---+   .   .
                    /             \   \   \
       .   .   +---+   +---+---+   +   +   +   .   .
              /         \       \   \ /    49
     .   .   +   +---+   +---+   +   +   .   .   .
              \   \   \     /   /
       .   .   +   +   +---+   +   +---+   .   .   .
                \ /             \ /   /10
     .   .   .   +   +---+---+   +   +   .   .   .
                 25   \       \     /9
       .   .   .   .   +---+   +---+   .   .   .   .
                          /    7   8
     .   .   .   .   +---+   .   .   .   .   .   .
                     0   1
- hence a(8) = a(9) = a(10) = a(50) = 3.

Prog

(PARI) See Links section.

Crossrefs

Cf. A334486 (Y coordinate), A229214 (directions +-1,2,3), A261180 (directions 0..5).

Sequence in context: A364367 A128080 A062187 * A347824 A031283 A293229

Adjacent sequences: A334482 A334483 A334484 * A334486 A334487 A334488

Keyword

sign,look

Author

Rémy Sigrist, May 03 2020

Status

approved