Egyptian fractal

[Antonio González]

Let us consider the sequence of Euclid numbers

  2,3,7,43....

(http://www.research.att.com/~njas/sequences/A000058)

that give an Egyptian expansion of unity

  1 = 1/2 + 1/3 + 1/7 + 1/43...

If we construct the set

  x = b1/2 + b2/3 + b3/7 + b4/43 + ...

where b_i can be either 0 or 1, we obtain a Cantor-like set on the 
interval [0,1]. Which is the fractal dimension of this set?
--
  Antonio