This puzzle is based off the What is a Word™, What is a Phrase™ and What is a Number™ series started by JLee.
If a number conforms to a certain rule, I call it a Self-Rejecting Number™. Use the following examples to find the rule:
Here is a CSV:
Self-Rejecting Numbers™,Non-Self-Rejecting Numbers™ 836,638 7192,9172 7912,1972 13930,13931 17272,27171 570988,988570 999670,666970 1811110,1111810 3123470,2432170 3432170,2123470 5555690,5555960 6035084,4805306
The puzzle relies on the series' inbuilt assumption, that each number can be tested for whether it is a Self-Rejecting Number™ without relying on the other numbers.
These are not the only examples of Self-Rejecting Numbers™, more can be found.
Hint 1 (small):
It is an open question in mathematics whether any are odd.