1) It is proper to call them "notes" and not "bills", right? 2) What are the rules that they use for printing the actual serial numbers? (i.e., they will never print one with the serial number "A00000000A", right?) This page at MoneyFactory.gov talks about the letters. Federal Reserve notes, beginning with Series 1996, have two letters rather than one at the beginning of the serial number. On these notes, the first letter corresponds to the series of the note and the second letter of each serial number now represents the issuing FRB and ranges from A through L. The last letter still can be anything but O or Z, and is still occasionally replaced by a star, with the same meaning as before. Up through Series 1995, all Federal Reserve notes had serial numbers consisting of one letter, eight digits, and one letter, such as A12345678B; now only the $1 and $2 notes still use this form. The letter O is not used because of its similarity to the digit 0, and the letter Z is not used because it is reserved for test printings. On some notes, a star appears in place of the last letter. The first letter of such a serial number identifies the Federal Reserve Bank (FRB) which issued the note; since there are 12 FRBs, this letter is always between A and L. The last letter advances through the alphabet when all eight character serial numbers have been printed for a specific Federal Reserve Bank within the same series. At the time of a series change, the suffix letter returns to the letter A and repeats the cycle. This page at OneDollarBill.org explains why each letter is chosen, as well as Series Date/Year, Plate Serial Number, Note Number Position, etc. But do they start at "00000001" and just count up from there? Do they ever print bills with all the same digit (e.g., "A11111111A"?)
1) Yes it is. Or "banknotes". 2) I don't believe I've ever heard of a serial number 0000000 note that wasn't a "specimen" (and therefore likely produced more than one of them). Not that all specimens have that serial. You can also see things like 12345678 as specimens. Outside of that, they start at 000001 and go up from there, including 111111 etc. Collectability for 0000001 is huge, of course.
Technically, note 00000001 is on the last sheet printed of the run, not the first. Numbering is done in reverse order so that the numerical sequence of the stacked sheets has the lower numbers on top.
They start at 00000001, yes. Denominations up to $20 are printed in runs of 6,400,000 notes, so after fifteen runs, the serialling is up to 96000000. At that point, there aren't enough serials left for another run, so they start over at 00000001 (and increment the suffix letter). The $50's and $100's are printed in runs of 3,200,000 notes, so they can fit thirty-one runs per block, and so the serials go up to 99200000. No serials higher than 99200000 have been printed for circulation since the '80s. But higher serials have sometimes been used for the uncut sheets the BEP sells to collectors. Decades ago, when the standard print runs were smaller, the serials printed for circulation went all the way to 99999999. "Fancy" serials like 11111111 are treated normally by the BEP (although they're likely to be intercepted by alert bank tellers before you have a chance to find them in circulation). For the past several decades, though, nearly all serials ending in 9999 or 0000, and many serials ending in 00002, were systematically pulled for quality-control testing (and replaced by star notes); this made certain specific serial numbers largely unavailable. Within the past few years, the BEP has started using newer equipment that samples notes randomly, rather than systematically, for quality control; thus those once-unavailable serials have been appearing in circulation again.
