Go away! No-1's Here! I was playing around with some numbers and found a sequence that, of course, is on OEIS. It is A005823: Numbers whose ternary expansion contains no 1's. It goes:


  a(2n) = 3*a(n)+2
  
  a(2n+1) = 3*a(n+1)
  
  a(1) = 0 
  
  a = 0,2,6,8,18,20,24,26,54....


I wrote a CJam program that generates the first n of these numbers by converting the index to binary, replacing the 1's with 2's, and converting from ternary to decimal.

I also noticed that any even number can be obtained by taking the sum of two numbers in the sequence (sometimes the number with itself). 

The Challenge:

Given any non-negative even number as input, output the indices of two numbers in the sequence that sum to it. (Note that sometimes multiple pairs are possible.) 

The Rules:


Specify if you're using 0- or 1-indexing.
If you're outputting as a string, put a delimiter between the two indices.
You are allowed to output as a complex number.
If you so desire, you can output every valid pair.
Code Golf: shortest answer wins


Test Cases

I use 0-indexing. Here I list every possible output for each input, but you only need to output one.


0:      [0 0]
2:      [1 0]
4:      [1 1]
6:      [2 0]
8:      [2 1]   [3 0]
10:     [3 1]
12:     [2 2]
14:     [3 2]
16:     [3 3]
18:     [4 0]
30:     [6 2]
32:     [6 3]   [7 2]
46:     [7 5]
50:     [7 6]
120:    [10 10]
338:    [19 18]
428:    [30 23] [31 22]
712:    [33 27] [35 25] [41 19] [43 17] [49 11] [51 9]  [57 3]  [59 1]
1016:   [38 37] [39 36] Thanks to @Luis Mendo for test case help.

Related: Is it within the Cantor set?
Husk, 21 14 13 bytes
-7 bytes, thanks to @Neil's JS answer
-1 byte inspired by betaveros's Parradoc answer
Uses 0-indexing
mḋTmMo±&gt;ḋ2B3½

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Explanation
            ½    Half the input
          B3     Convert to Base 3
   m             Map over the list
    Mo±&gt;ḋ2       Function such that: 0 -&gt; [0,0], 1 -&gt; [0,1], 2 -&gt; [1,1]
        ḋ2       Binary 2, [1,0]
    M            For each in that list
     o±&gt;         check if the argument is greater than it
  T              Transpose
mḋ               Convert each from binary

Previous 21 byte Solution
First time I've seen a use for ».
mḋT»o%2+ȯ?´eḋε%3`-0B3

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Longer, as I was dealing with carries