Sequence A112088 without example

[Max]

On 6/5/06, Rainer Rosenthal <r.rosenthal at web.de> wrote:
> To SeqFan and to author Simon Strandgaard:
>
> Playing the "Josephus problem" with "every third out"
> and denoting the minimum numbers in this game, I found
>
>      2, 3, 5, 7, 11, 16, 24, 36, 54, 81, ...
>
> I was happy to find them in this sequence:
> http://www.research.att.com/~njas/sequences/A112088.

The current definition of A112088 sounds cryptic.
What "binary tree" it is talking about?
And how does this tree depend on the index n?
I would be interested to hear a clear definition of A112088.

Thanks,
Max