How to construct a Turing machine for a language 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.
Try to come up with an algorithm, and then write the simplest possible program in some usual programming language for recognizing L. Then translate that program to a Turing machine.

N is not "in base 10" - it's just a number in your computer's memory, which is probably internally represented in base 2, but your program shouldn't care.

To check if a number contains 1 in base 3 representation, try to build the base-3 representation using the usual base conversion algorithm (digit = x mod 3, proceed with x div 3), and stop when you see a 1.