Sequence A112088 without example

[Rainer Rosenthal]

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.

My computed values are the same up to a(18) = 2082, so
that my Josephus game is likely to generate exactly
this sequence. I would like to make an appropriate
comment, but ... I don't understand how Simon generated
this sequence. There is some program code but there 
should be one example at least. I thought this to be
mandatory if you submit a sequence.

This is a typical SeqFan's case: you work on problem B
and via OEIS you suddenly realize a connection to some
problem A. Wonderful .... but what if you don't know
what problem A really is? Here: what kind of binary
trees are related to my Josephus game?

Best regards,
Rainer Rosenthal
r.rosenthal at web.de