A 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

posted over 3 years ago

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3y ago by General Sebast1an‭

caird coinheringaahing‭

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