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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()

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