To clear things up, "H" isn't the series letter, it's the indicator letter of the Kansas City Federal Reserve District that distributed the bill*
If the serial numbers don't match, you almost certainly have what's called a stuck-counter error. Depending on the bill's condition it could retail for $100 to $200.
How it happens:Serial numbers are printed by two mechanisms that work like the mechanical odometer on an old car. They're both supposed to click once per bill, but every so often one gets stuck and lags behind which causes the numbers to get out of synch.(*) FWIW, the bill wasn't printed in Kansas City. Back in 1977 all paper money was printed in Washington. Different print runs would be made depending on which Fed district orders the bills.
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I have a 2 dollar bill with Jefferson on it, serial number B 06184684 A. The 2's are in silver, the writing unites states of America, two dollars, and behind Jefferson's head are also in silver. What does this mean and what is the value, it is uncirculated, Series 2003 A with green seal.
There really aren't any "rare" serial numbers, all serial numbers are only used once on a particular denomination/issuing bank/series. The most in demand are the first notes and the last notes of each series. Also in demand are the ones with all consecutive numbers (such as the serial number being all 4s or 7s), also popular with some collectors are radar notes, notes with serial numbers that are the same backwards and forwards. Overall though, the paper money market is pretty cold right now and it is a lot harder to sell an interesting note, particularly a modern note with an interesting serial number than something like a rare coin.
Enormous numbers of $2 bills were printed in 1976 for the Bicentennial celebration, so it's not unusual to find them with consecutive serial numbers. If they're from change, they have no extra value. Uncirculated ones might bring $3 to $4.
Series letters for 1934 $20 bills only went up to "D". You may be looking at the Federal Reserve letter instead of the series letter. The series letter should be next to the date; it's also possible that there isn't any letter.There's more information at the Related Question.Serial NumbersIt's normally not necessary to provide a bill's serial number when asking about its value. Serial numbers are counters and a security feature but rarely affect a bill's value. Some collectors will pay extra for numbers with a special pattern, e.g. 12345678, or low numbers such as 00000015.
Serial numbers are counters and security features, but only affect a bill's value in specific cases. Normally the bill's series date and letter as well as its condition are much more important in determining a bill's value. Please post a new and separate question with that information.