For any nonzero complex number z we define a sequence a 1 ( z ) = z , a 2 ( z ) = z a 1 ( z ) , … , a n + 1 ( z ) = z a n ( z ) , n ∈ ℕ . We attempt to describe the set of these z for which the sequence { a n ( z ) } is convergent. While it is almost impossible to characterize this convergence set in the complex plane 𝒞 , we achieved it for positive reals. We also discussed some connection to the Euler's functional equation.