Although this is not a proof, here is a thought. We can write any number in binary form by writing out 0's and 1's and use an additive operator. In other words, you write down any number as a_1*1+a_2*2+a_3*4+a_4*8+ and so on letting a_1, a_2, ... to be 0 or 1 to get any number. For the problem you pose, we extend that to 3 possible values for a_1, a_2, ... being -1, 0, 1 and the numbers instead of powers of two now are powers of 3.