Definition:Kaprekar Triple

From ProofWiki
Jump to navigation Jump to search

Definition

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Suppose that $n^3$, when expressed in number base $b$, can be split into three parts that add up to $n$.

Then $n$ is a Kaprekar triple for base $b$.


Sequence of Kaprekar Triples

The sequence of Kaprekar triples begins:

$1, 8, 45, 297, 2322, 2728, 4445, 4544, 4949, 5049, 5455, 5554, \ldots$


Examples

45

$45$ is a Kaprekar triple.


297

$297$ is a Kaprekar triple.


Also see


Source of Name

This entry was named for Dattathreya Ramchandra Kaprekar.


Sources