Richard's Paradox

This is one of the really cool paradox I came across. Find the fallacy in this paradox.

Consider the properties of natural numbers that can be described in, say, the english language. For instance, the property of a number being a prime can be described as "a number x that is not divisible by any other number other than 1 and itself". As an another example, the property of a number that has an integer square root can be described as "a number x that is a product of an integer by itself", etc. 

Now these descriptions can be listed one by one, based on the number of letters present in them. For example, the description "a number x that is not divisible by any other number other than 1 and itself" has 61 letters and the description "a number x that is a product of an integer by itself" has 41 letters and so the latter description will be listed before the former description. If two descriptions have the same number of letters then they can be arranged alphabetically in the order of appearance. 

Call a number x as Richardian if x does not satisfy the description listed in the x^th row. Thus, 41 is Richardian whereas 61 is not Richardian. 41 is Richardian since 41 does not have an integer square root and 61 is not Richardian since 61 is a prime number. Now this property of a natural number being Richardian that is described can then be listed in a row. Let the row number corresponding to this description be n.

The question is then "is n Richardian?"

If n is Richardian, then by definition it should not satisfy the description in the n^th row. But, the n^th row description is the definition of a Richardian number and so n will not be Richardian. On the other hand if n is not Richardian, then it does not satisfy the description on the n^th row and so it will be Richardian. Thus, n is Richardian if and only if it is not Richardian.

Isn't this cool? So what is the fallacy here?