Definition:Modified Kaprekar Mapping

Definition

The modified Kaprekar mapping is the arithmetic function $K: \Z_{>0} \to \Z_{>0}$ defined on the positive integers as follows:

Let $n \in \Z_{>0}$ be expressed in some number base $b$ (where $b$ is usually $10$).

Let $n'$ be the positive integer created by:

arranging the digits of $n$ into descending order of size

then:

exchanging the last two digits.

Let $n$ be the positive integer created by:

arranging the digits of $n$ into ascending order of size

then:

exchanging the first two digits.

Then:

$\map {K'} n = n' - n$

making sure to retain any leading zeroes to ensure that $\map K n$ has the same number of digits as $n$.

The modified Kaprekar mapping is reported by David Wells in his $1997$ work Curious and Interesting Numbers, 2nd ed. to appear in volume $22$ Journal of Recreational Mathematics on page $34$ in an article authored by Charles Wilderman Trigg, but this has not been corroborated.

The term modified Kaprekar mapping was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$ as a convenient way to refer to this mapping.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.