Use a generator function for the Calkin-Wilf sequence to determine where in the sequence a given rational number lies.

calkin_wilf_sequence.py

def calkin_wilf_sequence(number):
    def fractions():
        from fractions import Fraction
        i = Fraction(1/1)
        while True:
            yield [i.numerator, i.denominator]          
            i = Fraction(1 / (2*int(i) - i + 1))
            
    gen = fractions()
    res = 0
    while next(gen) != number:
        res += 1
    return res