The logical designation for the F-117 would be A-117 (not B, which is typically reserved for medium and heavy bombers).
AFAIK the A-10 was the last USAF
model to receive the designation, the A-12 the last USN
model (and that one was cancelled, A-7 was the last to reach production).
F is used for multi-role aircraft as well, so F-117 might have been given to fool people into thinking it has an air defense role as well (or who knows, maybe that was indeed the plan at the time but it didn't work).