Definition:Kaprekar Triple
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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
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $297$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $45$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $297$