where each is a digit of , is a very simple, standard iterator operating in the range , and is a position of a digit; thus “describes” itself.
For example, the integer 6210001000 written in base 10. It has six instances of the digit 0, two instances of the digit 1, a single instance of the digit 2, a single instance of the digit 6 and no instances of any other base 10 digits.
Base 4 might be the only base with two self-descriptive numbers, and . From base 7 onwards, every base has at least one self-descriptive number of the form . It has been proven that 6210001000 is the only self-descriptive number in base 10, but it’s not known if any higher bases have any self-descriptive numbers of any other form.
|Date of creation||2013-03-22 15:53:27|
|Last modified on||2013-03-22 15:53:27|
|Last modified by||PrimeFan (13766)|
|Synonym||self descriptive number|