Conjecture
 = e^{1/e})
where  = x)
such that 
Discussion
To evaluate f at real numbers, an extension of tetration is required, but to evaluate f at positive integers, only real-valued exponentiation is needed. Thus the sequence given by the solutions of the equations
, also known as eta (
). Numerical evidence indicates that this is true, as the solution for x in 
is approximately 1.44.
The conjecture is proven to be true. Search the forum for "TPID 6".
Discussion
To evaluate f at real numbers, an extension of tetration is required, but to evaluate f at positive integers, only real-valued exponentiation is needed. Thus the sequence given by the solutions of the equations
The conjecture is proven to be true. Search the forum for "TPID 6".