Their specific property is that the sum of their digits raised to themselves is the original number. With the number one, it works spectacularly and easily well.
After that, you’re in trouble.
It isn’t until you get to 3435 that things put themselves right (try it for yourself if you don’t believe us!). Here’s the proof – try it with any other number of which you care to think and it will simply not work.
Now to proof that isn’t that straight forward … As usual programmers showed their brut force mentality and just tried them all … all?