> On 5 Jul., 21:20, amy666 <tommy1...@hotmail.com>
> wrote:
> > ( only considering reals , imput and output )

> > A = 1,39865929053...

> > f(0) = f(1) = x_0
> > f(n) = exp(f(n-1)) - exp(f(n-2))

> > ( f(2) is thus always = 0 )

> > for some x_0 the sequence f(n) seems to diverge to
> oo and for others it seems bounded.

> > it seems that the sequence for 1 < x_0 < A is
> bounded.

> > and for larger x_0 > A it diverges to oo.

> > thus of course the big question is : do we have a
> closed form for A = 1,39865929053... ???

> > its a simple iteration , similar to tetration
> (especially when it diverges to oo ).

> > if we do not have closed form for A , do we at
> least have an equation for it ?

> > perhaps if we also allow tetration-like functions
> in our equation ?

> > such a simple construct , i missed something
> trivial ??

> > for large n ;
> > f(n) = exp(f(n-1)) - exp(f(n-2)) =
> > exp(f(n-1)) - exp(exp(f(n-3) - exp(f(n-4)))
> > etc

> > does that help ?

> > regards

> > tommy1729

> How did you arrive at your A?
> For me it does not look too obvious that e.g. x_0 =
> 100 should produce
> divergence -> +oo.

> After all (with spreadsheet precision), everything
> stays within the
> same up an down pattern
> for more than 150 steps before the inevitable
> happens.
> OTOH, this shows that we cannot be sure that some x_0
> < A really
> produces a bounded (from above) sequence just by
> numerical evidence of
> 10000 steps, say.