def run(n: int) -> list:

    # Incrementor variable for our group list comprehension.
    # This serves as the first number in each list of values
    # to test.
    base = 2

    while True:
        # Increment each value of a generated range
        group = [base + i for i in range(n)]

        # Run elements through out unique_prime_factors function
        # Append our target number to the end.
        checker = [upf_len(x) for x in group]
        checker.append(n)

        # If all numbers in the list are equal, return the group variable.
        if equality(checker):
            return group

        # Increment our base variable by 1
        base += 1