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self-describing numbers
A number is called self-describing if it has an even number of digits, so that the digits can be divided into adjacent pairs and pair truthfully declares that the number contains copies 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

Self-describing numbers can also be... (you may click on names or numbers and on + to get more values)