  We developed an algorithm that easily goes from one odd number to the next
odd number in binary representation for the reduced forward Collatz map
(Syracuse function). The algorithm indicates when an odd number can grow or
shrink to the next odd number based on the pattern of binary digits. The
algorithm is also used to provide a simpler method for determining the change
in binary string length for the reduced map than one found in the literature.
Accordingly, an inspection of the binary digits for an odd number can determine
the number of binary digits of the subsequent odd number. We also show some
simple results for what the smallest number could be for a counterexample to
the Collatz conjecture.
