Keep whatever you like. Nobody can stop you. Just try to keep in mind that what you may think is 'collectible' might not always jive with what others think is 'collectible.'
As far as
fancy serial numbers go, typically birth-year or birthday notes have all the digits together. So if you want to commemorate 2020-2021 than the number would normally be:
0002020 or 0002021
['
Fancy' numbers, IMO, are numbers that are special to you so they may be a bit more of a specialty or niche collector's thing].
Here's a link to an American table on
Special serial numbers. It's a bit different than what we collect in Canada (since they use 8 digits & we have 7). Some people collect "near solids" but I think they're a bit more popular there & I really don't hear much about quads & other
ebay terms here as much.
http://goccf.com/t/407793#3495924[
Special serial numbers are well defined & can be found at the back of catalogues & usually every collector will agree that they're rare & desirable]