I was just counting using "whole" letters A-G. Trying to keep it simple...but then I threw you a curve.
So, yes, you're correct-
F(1) - G(2) - A(3) - Bb(4) - etc...
Back in my college theory daze, prof. would say something like F to A#...what's the interval?
Instinctively, I would think F to A# on my bass...I processed A# as Bb pretty much 100% back then. So, when I piped in that it was a Perfect 4th...WRONG!
Sounded like a Perfect 4th.
Theoretically, it's a raised 3rd.
Couldn't count to 3 back then, I guess.