An interesting sequence

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So I have an interesting sequence that I'm trying to find some kind of equation for (or at least a method of being able to predict the Nth value). The reason I can explain in a private message if anyone cares to know, and manages to find a solution, but I just wanted to ask here since I'm just above Grade 11 math, so I hoped someone may have better insight into what it could be. The sequence is:

0 1 2 4 5 7 8 10 13 14 17 19 20 22 25 28 29 32 34 35 38 40 43 47 49.....

One detail to note right from the start is that it entirely excludes ALL multiples of 3. That I am already quite sure will always be true in the sequence, though other numbers like 11 and 16 also are absent.

 

[pka]

So I have an interesting sequence that I'm trying to find some kind of equation for (or at least a method of being able to predict the Nth value). The reason I can explain in a private message if anyone cares to know, and manages to find a solution, but I just wanted to ask here since I'm just above Grade 11 math, so I hoped someone may have better insight into what it could be. The sequence is:

0 1 2 4 5 7 8 10 13 14 17 19 20 22 25 28 29 32 34 35 38 40 43 47 49.....

One detail to note right from the start is that it entirely excludes ALL multiples of 3. That I am already quite sure will always be true in the sequence, though other numbers like 11 and 16 also are absent.

Have a look HERE

 

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Have a look HERE

Dang. I had hoped that the result itself wouldn't involve primes itself. I have a second sequence that I derived this one from from which I can use to predict the value after every third term with complete accuracy, but unless I can predict the terms in between, it doesn't help much. Thanks!