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I'd approach this 'logically' - all numbers are going to be compilations of a small subset of number words - one to twenty, thirty, forty, fifty, hundred, thousand, million, billion.
I've eliminated the 'tens' that just have a y on the end, I don't need to worry about 'and' in large compound numbers as it's covered in 'thousand', but I don't know whether you are counting 'zero' as valid. (And if I thought about 0 too long, I could probably come up with a list of 'recognised names' to ask that question about...)
Now all I have to do is check each of the 26 letters of the English alphabet to see which are not used in my shortlist. Since I have decided unilaterally that zero is in the list (which makes your 'gazillion' a furphy, Mav), I end up with the following unused letters:
cjkpq
Let me know how close I am. (And BTW yes, I have realised now I could have missed out half the teens from my shortlist as well!)
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