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a(n) is the X-coordinate of the n-th point of Gosper's flowsnake curve; sequence A334486 gives Y-coordinates.
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%I #23 Feb 07 2021 09:49:03

%S 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,

%T -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,

%U 4,5,6,6,6,5,5,4,4,5,5,5,4,4,3,3,2,1,0,1,2,2,1,1

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

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

%C Y

%C /

%C /

%C 0 ---- X

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

%H Rémy Sigrist, <a href="/A334485/b334485.txt">Table of n, a(n) for n = 0..2401</a>

%H Rémy Sigrist, <a href="/A334485/a334485.png">Colored scatterplot of the first 7^7+1 points of the Gosper curve</a> (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)

%H Rémy Sigrist, <a href="/A334485/a334485.gp.txt">PARI program for A334485</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gosper_curve">Gosper curve</a>

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

%e The Gosper curve starts (on a hexagonal lattice) as follows:

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

%e \ \

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

%e \ \ / /

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

%e / \ \ \

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

%e / \ \ \ / 49

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

%e \ \ \ / /

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

%e \ / \ / /10

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

%e 25 \ \ /9

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

%e / 7 8

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

%e 0 1

%e - hence a(8) = a(9) = a(10) = a(50) = 3.

%o (PARI) See Links section.

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

%K sign,look

%O 0,8

%A _Rémy Sigrist_, May 03 2020