Search a number
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)