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a(n) is the X-coordinate of the n-th point of the R5 dragon curve; A349196 gives Y-coordinates.
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%I #16 Nov 14 2021 12:33:38

%S 0,1,1,0,0,1,1,0,0,-1,-1,-2,-2,-1,-1,-2,-2,-3,-3,-4,-4,-3,-3,-4,-4,-3,

%T -3,-4,-4,-5,-5,-6,-6,-5,-5,-6,-6,-5,-5,-4,-4,-5,-5,-4,-4,-5,-5,-6,-6,

%U -7,-7,-8,-8,-7,-7,-8,-8,-7,-7,-6,-6,-5,-5,-6,-6,-5,-5

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

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

%H Rémy Sigrist, <a href="/A349195/b349195.txt">Table of n, a(n) for n = 0..3125</a>

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 1.31.5 Dragon curves based on radix-R counting.

%H Kevin Ryde, <a href="http://user42.tuxfamily.org/r5dragon/index.html">Iterations of the R5 Dragon Curve</a>, see index "point".

%H Rémy Sigrist, <a href="/A349195/a349195.png">Colored representation of the first 1 + 5^9 points of the R5 dragon curve</a> (where the hue is function of the number of steps from the origin)

%H Rémy Sigrist, <a href="/A349195/a349195_1.gp.txt">PARI program for A349195</a>

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

%F a(5^k) = A006495(k) for any k >= 0.

%e The R5 dragon curve starts as follows:

%e +-----+

%e 24| 25

%e |

%e |

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

%e 23 22| 11| 10| 7| 6|

%e | | | | |

%e 21| 12| 9| 8| |

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

%e 20| 17| 16| 13| 4| 5

%e | | | | |

%e | | | | |

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

%e 19 18 15 14 3 2|

%e |

%e |

%e +-----+

%e 0 1

%e - so a(0) = a(3) = a(4) = a(7) = a(8) = 0,

%e a(1) = a(2) = a(5) = a(6) = 1,

%e a(9) = a(10) = a(13) = a(14) = -1.

%o (PARI) See Links section.

%Y Cf. A006495, A349008, A349009, A349010, A349196.

%K sign

%O 0,12

%A _Rémy Sigrist_, Nov 10 2021