A mammoth counting!

The main idea is to identify few numbers whose representations cannot be created using representations of other numbers. After a little thought, it is easy to see that only such numbers below $10000$ are $1$ to $20$ , $30, 40, 50, 60, 70, 80, 90, 100, 1000$ . For our problem, HUNDRED and HUNDREDS are same since the last S does not contribute anything. Below is the python function which returns the upper case English representation of a given natural number. After that, finding the actual truthful numbers is quite easy. There are only two: $16$ and $29$ . Hence the answer is $\boxed{45}$ .

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def number_to_name(s):    
    # Basic numbers
    basic_numbers = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 30, 40, 50, 60, 70, 80, 90, 100]
    # Basic names
    basic_names_small = [' ', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine', 'ten', 'eleven', 'twelve', 'thirteen', 'fourteen', 'fifteen', 'sixteen', 'seventeen', 'eighteen', 'nineteen', 'twenty', 'thirty', 'forty', 'fifty', 'sixty', 'seventy', 'eighty', 'ninety', 'hundred']

    basic_names = [name.upper() for name in basic_names_small]

    basic_map = {}
    for n, name in zip(basic_numbers, basic_names):
        basic_map[n] = name

    current_string = s
    if s in basic_numbers:    
        return basic_map[s]   
    else:
        s1 = ''; s2 = ''; s3 = ''
        # First describe the last two digits
        last_two = str(s)[-2:]
        if last_two[0] == 0:
            s1 = basic_map[int(last_two[1])]
        elif int(last_two) in basic_numbers:
            s1 = basic_map[int(last_two)]
        else:
            s1 = basic_map[int(last_two[0]) * 10] + ' ' + basic_map[int(last_two[1])]

        # Describe the remaining number
        remaining = (str(s)[:-2])
        for i, d in enumerate(reversed(remaining)):
            if i == 0 and d != '0':
                if int(d) == 1:
                    s2 = "ONE HUNDRED"
                else:
                    s2 = basic_map[int(d)] + " HUNDREDS"
            elif i == 1 and d != '0':
                if int(d) == 1:
                    s3 = "ONE THOUSAND"
                else:
                    s3 = basic_map[int(d)] + " THOUSANDS"

        return s3 + ' ' + s2 + ' ' + s1