def sum_numerator_fraction_expansion_e(x):
    """
    Returns the digit sum of the numerator of the x-th continued fraction of e
    """
    numerator = 1
    if x % 3 == 2:
        denominator = 2*(x//3 + 1)
    else:
        denominator = 1
    while x > 1:
        if x % 3 == 0:
            numerator += 2*(x//3)*denominator
        else:
            numerator += denominator
        numerator, denominator = denominator, numerator
        x -= 1
    numerator += 2*denominator
    digits = [int(i) for i in str(numerator)]
    return(sum(digits))