Euler #64

def propagate(root):
    approximate, numerator, period, seen = int(root**0.5), 1, 0, []
    modifier = approximate
    while True:
        denominator = root - modifier**2
        denominator /= numerator
        modifier *= -1
        modifier -= int((modifier+approximate)/denominator)*denominator
        numerator = denominator
        if [numerator, denominator, modifier] in seen:
            return period % 2 == 1
        period += 1
        seen.append([numerator, denominator, modifier])


answer = 0
testlist = [x for x in range(2, 10**4+1) if int(x**0.5) != x**0.5]
for x in testlist:
    if propagate(x):
        answer += 1
print(answer)