[I'm sure we have had this problem here previously, but I can't locate it.]
To start you off, let
. Then
. But the sequence is increasing, and
, so it follows that
. In other words,
. Therefore the only possibility is that
.
Thus
and
. Therefore
, and
. But if
and
then
and
have to fit in between 6 and 9 (because the sequence is increasing). The only way that can happen is if
and
.
Continue exploring in that way, using the facts that
and that the sequence is increasing. You will find that
is uniquely determined for each
. After a while, a pattern should emerge, which will enable you to predict
and