I had originally read the wp description and noted that there is a main part to testing if a number is in the series:

In mathematics, aThat is, splitting the ordered digits of the square of the number into two parts that sum to the original number.Kaprekar numberfor a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again. For instance, 45 is a Kaprekar number, because 45² = 2025 and 20+25 = 45.

Wikipedia then goes on to state that runs of all zeros are

*not*considered positive integers and so 100*100 = 10,000 and 100 + 000 = 100 is

*disallowed*.

What got me was tha

__t 1 is considered a member of the series__. The only way I could shoe-horn it into the general rule is to allow "splitting" the digits of the square before the first or after the last digit and so producing a number with no digits in it as a partial sum that

**is**allowed and has value zero?!

I widened my references and took a look at the Wolfram Mathworld entry. Its explanation for the series does not allow for 1 being a member, but shows it as such anyway. It is confused as it describes a series that would exclude numbers

`4879 and 5292`, i.e. Sloanes

`A053816`; but points to Sloanes A006886!

Sloanes

`A006886`gives another definition for the series:

Kaprekar numbers: n such that n=q+r and n^2=q*10^m+r, for some m >= 1, q>=0 and 0<=r<10^m, with n != 10^a, a>=1.If we try n = 1 then n*n = 1 and there is no m, q, and r that satisfies all the conditions.

I will submit a comment to Mathworld and see what they have to say.

P.S. I could have started this blog entry: "I'm not a mathematician but ..."