All digits must be accounted for, but pairs can be repeated.
For example, the number is divided into the pairs , , , , this say: the number contains three , one , one and three . Another example, the number , divided into , , tells us (twice) that it contains four .
The self-describing numbers are not very common. Up to (actually up to , since they must have an even number of digits) there are 783343 such numbers.
The smallest pandigital one is 10141516181923273271.
The self-describing numbers are finite, since we can have at most 9 copies of each digit. According to Robert G. Wilson the last term could be