def stable_expansion(digits, n):
values = continued_fraction_cycle(n)
h_values = [1, values[0]] # a_0
k_values = [0, 1]
cycle_length = len(values) - 1 # we only cycle over a_1,...,a_{k-1}
last = expanded_digits(h_values[1], k_values[1], digits)
index = 1
relation = [1, values[index]]
h_values = recurrence_next(relation, h_values)
k_values = recurrence_next(relation, k_values)
current = expanded_digits(h_values[1], k_values[1], digits)
while current != last:
index += 1
last = current
relative_index = ((index - 1) % cycle_length) + 1
# we want residues 1,..,k-1 instead of the traditional 0,...,k-2
relation = [1, values[relative_index]]
h_values = recurrence_next(relation, h_values)
k_values = recurrence_next(relation, k_values)
current = expanded_digits(h_values[1], k_values[1], digits)
return current
def main(verbose=False):
non_squares = [num for num in range(1, 10000 + 1)
if not is_power(num, 2)]
cycle_lengths = [len(continued_fraction_cycle(num)) - 1
for num in non_squares]
return len([num for num in cycle_lengths if num % 2 == 1])
