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Juggler sequences

A [Juggler sequence](https://en.wikipedia.org/wiki/Juggler_sequence) is a sequence that begins with a positive integer \$a_0\$ and each subsequent term is calculated as:
$$a_{k+1} = \begin{cases}
\left \lfloor a_k ^ \frac 1 2 \right \rfloor, & \text{if } a_k \text{ is even}\\\\\
\left \lfloor a_k ^ \frac 3 2 \right \rfloor, & \text{if } a_k \text{ is odd}
\end{cases}$$
Eventually, once \$a_k\$ equals \$1\$, the sequence ends, as all subsequent terms will be \$1\$. It has been conjectured, but not proven, that all Juggler sequences reach 1.
Given a positive integer \$n \ge 2\$, output the Juggler sequence beginning with \$a_0 = n\$ and ending in \$1\$. You may assume it will always terminate. You should only output a single \$1\$, and the sequence should be in calculated order (\$a_0, a_1, a_2,\$ etc.)
~~This is code golf, so the shortest code in bytes wins~~
---
## Test cases
```
2: 2, 1
3: 3, 5, 11, 36, 6, 2, 1
4: 4, 2, 1
5: 5, 11, 36, 6, 2, 1
6: 6, 2, 1
7: 7, 18, 4, 2, 1
8: 8, 2, 1
9: 9, 27, 140, 11, 36, 6, 2, 1
10: 10, 3, 5, 11, 36, 6, 2, 1
```

A [Juggler sequence](https://en.wikipedia.org/wiki/Juggler_sequence) is a sequence that begins with a positive integer \$a_0\$ and each subsequent term is calculated as:
$$a_{k+1} = \begin{cases}
\left \lfloor a_k ^ \frac 1 2 \right \rfloor, & \text{if } a_k \text{ is even}\\\\\
\left \lfloor a_k ^ \frac 3 2 \right \rfloor, & \text{if } a_k \text{ is odd}
\end{cases}$$
Eventually, once \$a_k\$ equals \$1\$, the sequence ends, as all subsequent terms will be \$1\$. It has been conjectured, but not proven, that all Juggler sequences reach 1.
Given a positive integer \$n \ge 2\$, output the Juggler sequence beginning with \$a_0 = n\$ and ending in \$1\$. You may assume it will always terminate. You should only output a single \$1\$, and the sequence should be in calculated order (\$a_0, a_1, a_2,\$ etc.)
This is <a class="badge is-tag">code-golf</a>, so the shortest code in bytes wins
---
## Test cases
```
2: 2, 1
3: 3, 5, 11, 36, 6, 2, 1
4: 4, 2, 1
5: 5, 11, 36, 6, 2, 1
6: 6, 2, 1
7: 7, 18, 4, 2, 1
8: 8, 2, 1
9: 9, 27, 140, 11, 36, 6, 2, 1
10: 10, 3, 5, 11, 36, 6, 2, 1
```

code-golf math number sequence