Verify Gen's hypothesis on September 23, 2022

verify20220923.py

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
#
# verify20220923.py
#
# Copyright (c) 2022 shihashi
#

from collections.abc import Sequence

N_MAX = 25

def get_sign_list(n: int) -> Sequence[int]:
    sign_list = [-1]
    for i in range(1, n):
        sign_list.append(sign_list[i // 2] * (1 - 2 * (i % 2)))
    return sign_list

def main():
    n_max = N_MAX
    sign_tuple = tuple(get_sign_list(2 ** (n_max + 1)))
    for n in range(1, n_max + 1):
        sum = 0
        for i in range(1, 2 ** (n+1)):
            sum += sign_tuple[i] * (i ** n)
        print(f'{n}: {sum}')

if __name__ == '__main__':
    main()