I have proved that language $L$ is not regular and think that it is recognizable by a Turing machine. I want to prove it by constructing a Turing machine for it.   $L=\{0^n|n \in A\}$where $A$ is set of all numbers that do not contain 1 in their base 3 representation. However, n is in base 10.  What I have done so far:When I was proving that the language is not regular, I used the fact that there cannot be any arithmetic sequences in A. I think if I work on the number of 1 in base three, I may get somewhere.If you have any ideas or hints, please help me.
How to construct a turing machine for a language
turing machines