#pi_approxs.py
#find "good" fractional approximations to PI, e.g. 22/7, 333/106, 355/113,

import  math

#IGNORE
def len_same_prefix(pi_approx):
    pi_str = str(math.pi)
    pi_approx = str(pi_approx)
    #print(pi_str, len(pi_str), len(pi_approx))
    digits = 1
    while digits<len(pi_str) and digits<len(pi_approx) and \
          pi_approx[0:digits+2]==pi_str[0:digits+2]:
        digits += 1
    return digits
    


close_enough = float(input("Enter how close to PI is good enough for you: "))

max_range = int(input("Enter the upper limit: "))

#try every combo of numerator and denominator (less than numerator)
# i.e. all improper fractions
for i in range(1,max_range+1):
    for j in range(1,i):
        if abs(i/j - math.pi) <= close_enough:   #difference between this fraction and PI is small enough
            print(i,j, i/j, len_same_prefix(i/j))