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

Author

Robert G. Wilson v, Sep 08 2014

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A014577, A106665.

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

Programs

Mathematica

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

Python

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

Formula

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

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