Keith Number/Examples/251,133,297

Examples of Keith Number
$251 \, 133 \, 297$ is a Keith number:
 * $2, 5, 1, 1, 3, 3, 2, 9, 7, \ldots, $

Proof
By definition of Keith number, we create a Fibonacci-like sequence $K$ from $\left({2, 5, 1, 1, 3, 3, 2, 9, 7}\right)$:

Thus $251 \, 233 \, 297$ occurs in $K$ and the result follows by definition of Keith number.