Odometer Game Redux

Well, after 35 years of pondering what I thought was an abstract mathematical puzzle, my "odometer game" has found a real-world application!

It turns out that my notion of "remarkable" numbers [i.e. numbers that are so remarkable that if the driver saw his odometer sitting on that number he would either honk his horn or point it out to his passengers] are just the ticket for finding "fake" ID numbers.

My current contract at a major bank found me looking for suspect ID numbers, Tax IDs, phone numbers, etc. in various customer databases. The bank employees entering this information would often get around the fact that these fields were "required" via entry of syntactically legal digit strings that were none the less meaningless. After viewing a few of these it quickly became obvious that they were related to my notion of remarkableness. Actual values found included: 0, 121212121, 000000000, 999999999(9), 111111111, 111111112, 222222221, 888888889, 188888888, 0999999999, 589999999, 255511555 (?)

So, rather than an explicit list of IDs to put on a watch list (as I was asked to find), it became clear that a better answer would have been to use an evaluation function that reported the remarkableness score for each value. A cutoff point could then be established to filter out suspicious values. Alas, while I have casually pondered the mathematics involved in scoring the remarkableness of a number, I've never actually tried to program it. But, now it has become more than an obscure puzzle, and shows signs of having "real world" value!