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```
"""
== Juggler Sequence ==
Juggler sequence start with any positive integer n. The next term is
obtained as follows:
If n term is even, the next term is floor value of square root of n .
If n is odd, the next term is floor value of 3 time the square root of n.
https://en.wikipedia.org/wiki/Juggler_sequence
"""
# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
import math
def juggler_sequence(number: int) -> list[int]:
"""
>>> juggler_sequence(0)
Traceback (most recent call last):
...
ValueError: Input value of [number=0] must be a positive integer
>>> juggler_sequence(1)
[1]
>>> juggler_sequence(2)
[2, 1]
>>> juggler_sequence(3)
[3, 5, 11, 36, 6, 2, 1]
>>> juggler_sequence(5)
[5, 11, 36, 6, 2, 1]
>>> juggler_sequence(10)
[10, 3, 5, 11, 36, 6, 2, 1]
>>> juggler_sequence(25)
[25, 125, 1397, 52214, 228, 15, 58, 7, 18, 4, 2, 1]
>>> juggler_sequence(6.0)
Traceback (most recent call last):
...
TypeError: Input value of [number=6.0] must be an integer
>>> juggler_sequence(-1)
Traceback (most recent call last):
...
ValueError: Input value of [number=-1] must be a positive integer
"""
if not isinstance(number, int):
msg = f"Input value of [number={number}] must be an integer"
raise TypeError(msg)
if number < 1:
msg = f"Input value of [number={number}] must be a positive integer"
raise ValueError(msg)
sequence = [number]
while number != 1:
if number % 2 == 0:
number = math.floor(math.sqrt(number))
else:
number = math.floor(
math.sqrt(number) * math.sqrt(number) * math.sqrt(number)
)
sequence.append(number)
return sequence
if __name__ == "__main__":
import doctest
doctest.testmod()
```