I always heard reducing a string of numbers down to a single digit was known as numerology.
As far as 3+9=11, that what you get when you buy a dozen eggs from Mr. Haney.
A bakers dozen is 13, Haney you get 11.
/ sum of serial numbers on a dollar bill - what's the term?
There is such a thing as a "check sum" or "check digit" that you can use to verify long numbers or sequences, but I don't think your process is either one. But in many vehicle VINs, there will be a check digit. Can be used to verify that a VIN is not fake.
/ sum of serial numbers on a dollar bill - what's the term?