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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.

%I A334485 #23 Feb 07 2021 09:49:03
%S A334485 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 A334485 -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 A334485 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 A334485 a(n) is the X-coordinate of the n-th point of Gosper's flowsnake curve; sequence A334486 gives Y-coordinates.
%C A334485 Coordinates are given on a hexagonal lattice with X-axis and Y-axis as follows:
%C A334485            Y
%C A334485           /
%C A334485          /
%C A334485         0 ---- X
%C A334485 The Gosper curve can be represented using an L-system.
%H A334485 Rémy Sigrist, <a href="/A334485/b334485.txt">Table of n, a(n) for n = 0..2401</a>
%H A334485 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 A334485 Rémy Sigrist, <a href="/A334485/a334485.gp.txt">PARI program for A334485</a>
%H A334485 Wikipedia, <a href="https://en.wikipedia.org/wiki/Gosper_curve">Gosper curve</a>
%H A334485 <a href="/index/Con#coordinates_2D_curves">Index entries for sequences related to coordinates of 2D curves</a>
%e A334485 The Gosper curve starts (on a hexagonal lattice) as follows:
%e A334485      .   .   .   .   .   +---+---+   .   .   .   .
%e A334485                           \       \
%e A334485        .   .   +---+---+   +---+   +   .   .   .   .
%e A334485                 \       \     /   /
%e A334485      .   .   .   +---+   +---+   +   +---+   .   .
%e A334485                     /             \   \   \
%e A334485        .   .   +---+   +---+---+   +   +   +   .   .
%e A334485               /         \       \   \ /    49
%e A334485      .   .   +   +---+   +---+   +   +   .   .   .
%e A334485               \   \   \     /   /
%e A334485        .   .   +   +   +---+   +   +---+   .   .   .
%e A334485                 \ /             \ /   /10
%e A334485      .   .   .   +   +---+---+   +   +   .   .   .
%e A334485                  25   \       \     /9
%e A334485        .   .   .   .   +---+   +---+   .   .   .   .
%e A334485                           /    7   8
%e A334485      .   .   .   .   +---+   .   .   .   .   .   .
%e A334485                      0   1
%e A334485 - hence a(8) = a(9) = a(10) = a(50) = 3.
%o A334485 (PARI) See Links section.
%Y A334485 Cf. A334486 (Y coordinate), A229214 (directions +-1,2,3), A261180 (directions 0..5).
%K A334485 sign,look
%O A334485 0,8
%A A334485 _Rémy Sigrist_, May 03 2020