MathDB

A positive integer

m

is called self-descriptive in base

b

, where

b\ge2

is an integer, if
i) The representation of

m

in base

b

is of the form

(a_0a_1\ldots a_{b-1})_b

(that is

m=a_0b^{b-1}+a_1b^{b-2}+\ldots+a_{b-2}b+a_{b-1}

, where

0\le a_i\le b-1

are integers). ii)

a_i

is equal to the number of occurences of the number

i

in the sequence

(a_0a_1\ldots a_{b-1})

.
For example,

(1210)_4

is self-descriptive in base

4

, because it has four digits and contains one

0

, two

1

s, one

2

and no

3

Problem Statement