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