I learnt about this phenomenon when I was at University. It has to do with how our brains automatically process memory.

How often do you look at the time on your watch/clock/phone then seconds later have to look again because you already forgot what it was? It happens all the time. That's because your brain is constantly making choices as to what to place in it's long term memory, and what to just keep temporarily in short term memory. In general the time is processed as quite low priority due to it's changing manner and the brain delegates it to short term memory. Times like 1:23 and 11:11 are more interesting than say 9:28, so your brain ranks it with a higher importance and might pop it into long term memory. Then next time when you see those numbers again you remember the last time because it is in your long term memory (whereas the next time you see 9.28 you no longer have the specific memory of the last time you saw it). Also, our brain is absolutely amazing at filtering what it thinks you should "notice" and what you don't need to. You'd be amazed how many things your eyes see each day that the brain filters out and you would never even know that you saw them.


EDIT: Just wanted to add that even though I believe in the science behind this phenomenon, I also believe that if certain numbers are important/special to you, then because of that your brain may also rank a memory of seeing those numbers as important and put that memory into the long term memory as well. Just didn't want to discount anyone's beliefs about the importance on numbers in their lives