There are only 9039 such numbers below one million, however there are infinite nude numbers since all repdigits are nude.
The smallest nude number which contains all the odd digits is 1117935. Note that if a nude number contains a `5', then all the other digits must be odd.
The smallest nude which contains the maximal (8) number of distinct digits is 1123449768. The smallest triple of consecutive nontrivial nude numbers is (1111, 1112, 1113). It is easy to see that there cannot be 4 consecutive nude numbers greater than 10.
The smallest 3 × 3 magic square whose entries are nontrivial consecutive nude numbers is