A246960 Directions of the lines in the (Heighway) Dragon Curve.

0, 1, 2, 1, 2, 3, 2, 1, 2, 3, 0, 3, 2, 3, 2, 1, 2, 3, 0, 3, 0, 1, 0, 3, 2, 3, 0, 3, 2, 3, 2, 1, 2, 3, 0, 3, 0, 1, 0, 3, 0, 1, 2, 1, 0, 1, 0, 3, 2, 3, 0, 3, 0, 1, 0, 3, 2, 3, 0, 3, 2, 3, 2, 1, 2, 3, 0, 3, 0, 1, 0, 3, 0, 1, 2, 1, 0, 1, 0, 3, 0, 1, 2, 1, 2, 3, 2, 1, 0, 1, 2, 1, 0, 1, 0, 3, 2, 3, 0, 3, 0, 1, 0, 3, 0

Offset

0,3

Comments

Fixed point of the morphism: 0 --> 01, 1 --> 21, 2 --> 23, 3 --> 03.

Links

Joerg Arndt, Table of n, a(n) for n = 0..16383

Joerg Arndt, Matters Computational (The Fxtbook), pp. 88-92; image of the dragon curve on p. 89 (top): 0 for north, 1 for west, 2 for south, and 3 for east.

Formula

a(n) = A005811(n) mod 4. - Joerg Arndt, Sep 09 2014

a(n) = A105500(n) - 1. - Filip Zaludek, Dec 16 2016

Mathematica

Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 1}, 2 -> {2, 3}, 3 -> {0, 3}}] &, {0}, 7]

Prog

(Python)
def A246960(n): return (n^(n>>1)).bit_count()&3 # Chai Wah Wu, Jul 13 2024

Crossrefs

Cf. A014577, A106665.

n where a(n) = 0,1,2,3 respectively: A043724, A043725, A043726, A043727.

Sequence in context: A338170 A066856 A089280 * A285200 A308567 A192099

Adjacent sequences: A246957 A246958 A246959 * A246961 A246962 A246963

Keyword

nonn,easy

Author

Robert G. Wilson v, Sep 08 2014

Status

approved