A numberis called self-describing if it has an even number of digits, so that the digits can be divided into adjacent pairsand pairtruthfully declares that the numbercontainscopies of digit

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

The first self-describing numbers are 22, 4444, 224444, 442244, 444422, 666666, 10123133, 10123331, 10143133, 10143331, 10153133 more terms