The number $128$ can be written as $2^n$ with integer $n$, and so can its every individual digit. Is this the only number with this property, apart from the one-digit numbers $1$, $2$, $4$ and $8$?

I have checked a lot, but I don’t know how to prove or disprove it.

**Answer**

This seems to be an open question. See OEIS sequence A130693 and references there.

**Attribution***Source : Link , Question Author : bifurcat , Answer Author : Robert Israel*