Python/maths/sylvester_sequence.py
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Co-authored-by: Dhruv Manilawala <dhruvmanila@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
2023-05-26 09:34:17 +02:00

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Python

"""
Calculates the nth number in Sylvester's sequence
Source:
https://en.wikipedia.org/wiki/Sylvester%27s_sequence
"""
def sylvester(number: int) -> int:
"""
:param number: nth number to calculate in the sequence
:return: the nth number in Sylvester's sequence
>>> sylvester(8)
113423713055421844361000443
>>> sylvester(-1)
Traceback (most recent call last):
...
ValueError: The input value of [n=-1] has to be > 0
>>> sylvester(8.0)
Traceback (most recent call last):
...
AssertionError: The input value of [n=8.0] is not an integer
"""
assert isinstance(number, int), f"The input value of [n={number}] is not an integer"
if number == 1:
return 2
elif number < 1:
msg = f"The input value of [n={number}] has to be > 0"
raise ValueError(msg)
else:
num = sylvester(number - 1)
lower = num - 1
upper = num
return lower * upper + 1
if __name__ == "__main__":
print(f"The 8th number in Sylvester's sequence: {sylvester(8)}")