, where each of the
's is either a 0 or a 1,
then there are
shorter strings ahead of 
in the list, while there are
strings smaller than
among the strings of length exactly 
.
Thus, appears as entry number
on our "big list."
on the list,
we begin by determining the length of the string at position
.
In order to simplify this
computation, let's first find an expression for the sum
of successive powers of 2. Notice that if we set
then
In other words, we must have
.
Now, given , we first trap it
between two such expressions; that is, we find
satisfying
or
(In other words, we find the base 2 logarithm of
+ 2). We know that
is a string of length
+ 1.
Finally, the th entry on
our list is the number
written as a binary string of length
+ 1.