Mathematical

Sieve of Erastothenes

def _squares(n):
    """
    Arguments:
        n (int): arbitray integer
        
    Returns:
        a list of squares up to the value of ``n``.
    """

    return [ 
        i*i 
        for i in range(1, n+1) 
        if i*i < n 
    ]

def primes(n):
    """
    Arguments:
        n (int): arbitrary integer
    Returns:
        A list of primes up to the values of ``n``
    """
    
    sqs = _squares(n)
    sieve = {
        x: True
        for x in range(2,n+1)
    }

    # NOTE: len(sqs) + 2 gives the next closest root of a perfect square
    for i in range(2, len(sqs) + 2):
        if sieve[i]:
            for j in range(1+1, n // i + 1):
                sieve[i*j] = False

    return [ k for k,v in sieve.items() if v ]

if __name__== "__main__":
    print(primes(300))

Recursive Sum of Squares

from typing import List, Union
import random 

def recursive_sum_of_squares(
    x: List[Union[float,int]], 
    checked: bool = False
) -> float:
    n = len(x)

    if not checked:
        if not all(
            this_x is not None and isinstance(
                this_x, 
                (float, int)
            ) for this_x in x
         ):
            raise ValueError(
                'Sample contains null values'
            )

        if n == 0:
            raise ValueError(
                'Sample variance cannot be computed for a sample size of 0.'
            )

    if n == 1:
        return 0

    term_variance = (n*x[-1] - sum(x))**2/(n*(n-1))
    return recursive_sum_of_squares(x[:-1], True) + term_variance

if __name__ == "__main__":
    sample = [
        random.randint(0, 100) 
        for _ in range(0,100)
    ]
    n = len(sample)
    variance = recursive_sum_of_squares(sample) / (n - 1)
    print(variance)