When you have a unique or highly specialized need (as your request is), it almost surely would have to be created with a script. If you're not a person who writes scripts, you may have to find if such a script has already been created, or if you're willing to pay someone to create one.
If you get no responses here, ask in the InDesign Scripting forum:
The poster wants to start at "F", not at "A". That means they'd have to do the same thing with A thru E. That's pretty awkward. A script would be better.
How often do you need this?
You might be better off creating your own "answer sheet" font that would have your own letters in the usual places for letters.
So, if you wanted the answers to start with the letter F, the font would put a capital F in the spot where capital A would be. And so on.
You would also be able to skip the capital letter I and go straight to J.
It wouldn't be hard, at all, to modify the font which would then be used as part of the character style for the numbered list. The easiest app to use is TypeTool from FontLab for either Mac or Windows. http://www.fontlab.com/font-editor/typetool/.
It wouldn't be difficult to do and would probably take an afternoon.
Interesting idea, but I think IndyFont, which is a script for ID, might be even easier to work with. You can try the demo at Adobe Community: [Ann] IndyFont Demo: make your own (1 character) font
The paid version would be required to do a set of numbers.
I thought about this font modification. I've done it a long time ago: it takes only a few minutes. open the font, copy the "F", paste in place of "A", then copy the "G", paste in place of "B", ... Save as as a new font. 20 manip. It is not complicated but risky for someone who has not used.
Not necessarily: just create 2 para styles: first, begins to F, and 2nd, for the letters that follow and the tip to jump the "J".
The price is so low that it does not bother to deny it. A very great tool I like!
I thought about IndyFont, which I own and adore! I used it to make a single-character of the word "TIP" which I use in my VQS book.
And IndyFont is cheaper than TypeTool.
But I would suggest TypeTool as it is slightly easier to use, especially for figuring out which character goes in which block.
But I think we all agree that a custom font is the way to go.