Dean¹s Word: Omega 2,1

[Ralf Stephan]

> > Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {2, 1}, 2 -> {0, 3}, 3 -> {2, 
> > 3}}] &, {0}, 7]
> > {0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 
> > 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 
> > 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 
> > 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 2, 1, 0, 1, 2, 1, 0, 3, 2, 3, 
> > 0, 1, 2, 3, 0, 3, 2, 3, 0, 1, 2, 1, 0, 3, 2, 1, 0, 1, 2, 3, 0, 3, 
> > 2, 3, 0, 1, 2, 1, 0, 3, 2, 3, 0, 1, 2, 3, 0, 3, 2, 1}
> 
> It should be easy to prove that
> 
>   a(4n) = 0, a(4n+2) = 2, a(8n+1) = 1, a(8n+5) = 3, 
>   a(4n+3) = a(2n+1).

Which also means that a(2n) = 2(n mod 2), a(2n+1) = 1 + 2*A014707(n), with
A014707(n) the classical paperfolding curve.


ralf