MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

4 deleted 44 characters in body

What is the Hausdorff dimension of the subset $$F := \{ x = \sum^\infty_{n=1} \frac{2 x_n}{3^n} \in [0,1] : x_n \in \{ 0 , 1 \} , x_n = 1 \Rightarrow x_{n+1}=0 \}$$ of the Cantor set? Is it known already?

As far as I know, this set can be corresponded to a binary tree related to the Fibonacci sequence. (I don't know how to call that tree.)

Edit: $x_n = 1 \Rightarrow x_{n+1}=0$.

3 added 44 characters in body

What is the Hausdorff dimension of the subset $$F := \{ x = \sum^\infty_{n=1} \frac{2 x_n}{3^n} \in [0,1] : x_n \in \{ 0 , 1 \} , x_n = 1 \Rightarrow x_{n+1}=0 \}$$ of the Cantor set? Is it known already?

As far as I know, this set can be corresponded to a binary tree related to the Fibonacci sequence. (I don't know how to call that tree.)

Edit: $x_n = 1 \Rightarrow x_{n+1}=0$.

2 added 4 characters in body

What is the Hausdorff dimension of the subset $$F := \{ x = \sum^\infty_{n=1} \frac{2 x_n}{3^n} \in [0,1] : x_n \in \{ 0 , 1 \} , x_n = 1 \Rightarrow x_n=0 x_{n+1}=0 \}$$ of the Cantor set? Is it known already?

As far as I know, this set can be corresponded to a binary tree related to the Fibonacci sequence. (I don't know how to call that tree.)

1