1. For each integer a_0 > 1, define the sequence
a_0, a_1, a_2, ... for n >= 0 as
a_{n+1} = sqrt(a_n) if sqrt(a_n) is an integer,
a_n + 3 otherwise.
Determine all values of a_0 such that there exists
a number A such that a_n = A for infinitely many values
of n.
2. Let R be the set of real numbers. Determine all
functions f: R