TheAlgorithms-Python

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