thegamesbond
Do near-misses like these count?
No: just think horseshoes & hand grenades. The number is either on (or off).
The sequential note you mentioned (such as 7654321) is called a Ladder serial. The example is a descending ladder. There are also ladder radars such as 1234321, or 4321234 which are very tough.
Another special # yet to be mentioned is the Rotator (some people call these “flippers”). A rotator is a number which looks identical when the note is rotated such as radar rotator 0888880 or simply a rotator 086980 (which can be really hard/tough to find). I know of collectors who seek the 2nd type much more avidly than the radar rotator (simply b/c so many collectors miss the 2nd type).
Another missed special number is the Million # note:
2000000, 3000000
In the US it would be a 10 Million # note or 10000000 which would be more expensive than a 7 digit Million # note b/c its tougher to obtain.
The general rule of thumb is that the less # of digits the less expensive (easier) the special serial number.
Some computer science people like what they call true binaries (0011001 or 0101001, etc). The serials are just 1's or zeros (not other digits) but unfortunately many people have confused the terms. For other digits (9090099, etc) I would call these 2 digit serial numbers & “fancy.”
I reserve the term “fancy” for a nice looking number with lots of zeroes, or one's area code, a birthdate note, etc. I don't start threads on “Fancy serial numbers” b/c there's so many sellers, social media posters who will call just about any number as fancy & rare to sell it. These are often the same people who call a poorly centred note an “error” when its just a poorly centred note.