If a number conforms to a certain rule, I call it an ES Number™. Otherwise, I call it an OS Number™ Use the following examples to find the rule:
Here is a CSV:
ES Numbers™,OS Numbers™ 4,5 96,48 343,434 2048,1024 15679,14679 86420,97531 1234567,6543210 543543543,210210210 3597175319,1354279860 8406268402,9068731254
The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is an ES Number™ or an OS Number™ on its own. In particular, a number's relationship to other numbers in the sequence is irrelevant.
These are not the only examples of ES or OS Numbers™, more can be found.
EDIT: SORRY TO EVERYONE WHO ATTEMPTED THIS PUZZLE
I made a mistake in my ES Numbers™ list. 24 is actually an OS Number™. In order to make something similar to the original, I have included 96 which is an ES Number™. Unfortunately this makes the puzzle less cruel. ;)
Once again, sorry for the time you may or may not have wasted. I double-checked the puzzle and still didn't pick up the mistake. Now it is solvable in the intended way. (I've triple checked that)