Balancing numbers

balance.py

import math

N = 10000000

def check_bm(n, r):
    lhs = (n*(n-1))//2
    rhs = n*r + (r*(r+1))//2
    return lhs == rhs

def list_bm():
    for n in range(0, N):
        d = 8*n*n + 1
        sqrtd = math.isqrt(d)
        if sqrtd * sqrtd != d:
            continue
        r = (-2*n-1 + sqrtd) // 2
        if not check_bm(n, r):
            print(f'n={n}; r={r}; oops...')
            continue
        print(f'n={n}; r={r}')

def check_ibm(n, r):
    lhs = (n*(n+1))//2
    rhs = n*r + (r*(r+1))//2
    return lhs == rhs

def list_ibm():
    for n in range(0, N):
        d = 8*n*n + 8*n + 1
        sqrtd = math.isqrt(d)
        if sqrtd * sqrtd != d:
            continue
        r = (-2*n-1 + sqrtd) // 2
        if not check_ibm(n, r):
            print(f'n={n}; r={r}; oops...')
            continue
        print(f'n={n}; r={r}')

if __name__ == '__main__':
    print('balanced numbers (not including n)')
    list_bm()
    print('balanced numbers (including n)')
    list_ibm()