Output the Juggler sequence The Juggler sequence is described as follows. Beginning with an input \$a_1\$, the next term is defined by the recurrence relation
$$a_{k+1} = \begin{cases}
\left\lfloor a_k ^ \frac 1 2 \right\rfloor,\text{ if } a_k \text{ is even} \\
\left\lfloor a_k ^ \frac 3 2 \right\rfloor,\text{ if } a_k \text{ is odd} \\
\end{cases}$$
The sequence terminates when it reaches 1, as all subsequent terms would then be 1.
Task
Given an input \$n\$ greater than or equal to 2, write a program/function/generator/etc. that outputs/returns the respective juggler sequence. The output can be in any reasonable form. You may not use a built-in that computes the juggler sequence, or any built-in that directly yields the result. You may assume that the sequence terminates in \$1\$.
Test Cases
Input: output
2: 2, 1
3: 3, 5, 11, 36, 6, 2, 1
4: 4, 2, 1
5: 5, 11, 36, 6, 2, 1

This is a code golf. Shortest code in bytes wins.
Julia, 64 50 48 42 32 30 bytes



g(x)=[x;x&lt;3||g(x^(x%2+.5)÷1)]


This is a recursive function that accepts an integer and returns a float array.

We build an array by concatenating the input with the next term of the sequence, computed as x to the power of its parity plus 1/2. This gives us either x1/2 or x1+1/2 = x3/2. Integer division by 1 gets the floor. When the condition x &lt; 3 is true, the final element will be a Boolean rather than a numeric value, but since the array is not of type Any, this is cast to have the same type as the rest of the array.

Saved 14 bytes thanks to Dennis!