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A334485
a(n) is the X-coordinate of the n-th point of Gosper's flowsnake curve; sequence A334486 gives Y-coordinates.
4
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, 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)
Wikipedia, Gosper curve
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
KEYWORD
sign,look
AUTHOR
Rémy Sigrist, May 03 2020
STATUS
approved