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:

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

which can alternatively be written as

$$H(n)={\begin{cases}{\frac {3n}{2}}&{\text{if }}n{\text{ even}}\\{\frac {3n-1}{2}}&{\text{if }}n{\text{ odd}}\\\end{cases}}$$

or simply

$$H(n)=\left\lfloor {\frac {3n}{2}}\right\rfloor$$

It has some connections to Mahler's 3/2 problem.