diff --git a/maths/juggler_sequence.py b/maths/juggler_sequence.py new file mode 100644 index 000000000..9daba8bc0 --- /dev/null +++ b/maths/juggler_sequence.py @@ -0,0 +1,61 @@ +""" +== 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): + raise TypeError(f"Input value of [number={number}] must be an integer") + if number < 1: + raise ValueError(f"Input value of [number={number}] must be a positive integer") + 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()