Replying to a query by Bob Solovay, Ron Graham wrote:
> This real is well known to be e^(1/e)
Just to comment that this number has a nostalgic interest for me. When I
was a freshman I managed to prove that the sequence defined by s_1=x,
s_{n+1} = x^(s_n) converges precisely for real numbers x satisfying (1/e)^e
<= x <= e^{1/e).
Martin