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Juggler sequences

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A Juggler sequence is a sequence that begins with a positive integer $a_{0}$ and each subsequent term is calculated as:

$a_{k + 1} = {\begin{cases} ⌊ a_{k}^{\frac{1}{2}} ⌋, & if a_{k} is even \\ ⌊ a_{k}^{\frac{3}{2}} ⌋, & if a_{k} is odd \end{cases}$

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 $n \geq 2$ , 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 almost 4 years ago

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3y ago by General Sebast1an‭

caird coinheringaahing‭

516 reputation 3 13 61 12

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