We investigate the size of the set of reals which can be represented in base γ using only the digits 0, 1, 3. It is shown that this set has Lebesgue measure zero for γ < 1/3 and equals an interval for γ >2/5. Our main goal is to prove that it has Lebesgue measure zero for a certain countable subset of (1/3, 2/5).
- Cantor sets
- Hausdorff dimension