'8237514874318 '

How is this phenomena called?

Numbers that represents themselves in binary when sliced to specific amount of bit numbers?

8-1000,
2-0010,
3-0011,
7-0111,
5-0101,
1-0001,
4-0100,
8-1000,
7-0111,
4-0100,
3-0011,
1-0001,
8-1000,

Wasn't some popular culture media piece about this kind of recursion?

How is this pattern behavior called?

Specific name for this 4bit stream, and specific for a representing itself as digits when different base is sliced to digits so there's still those digits?

Is it normal? In my option, not really, because if there's something different...

What's the probability of guessing number like this on random?