Hydra function

The Hydra function is a Collatz-like function whose behavior is connected to the the unsolved halting problems for the Cryptids Hydra and Antihydra:

$$\begin{array}{lll}H(2n)& =& 3n\\ H(2n+1)& =& 3n+1\\ \end{array}$$

which can alternatively be written as$$H(n)=\{\begin{array}{ll}\frac{3n}{2}& \text{if }n\text{ even}\\ \frac{3n-1}{2}& \text{if }n\text{ odd}\\ \end{array}$$or simply$$H(n)=\lfloor \frac{3n}{2}\rfloor$$It has some connections to Mahler's 3/2 problem.