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