Keith Number/Examples/197

Examples of Keith Number
$197$ is a Keith number:
 * $1, 9, 7, 17, 33, 57, 107, 197, \ldots$

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

Thus $197$ occurs in $K$ and the result follows by definition of Keith number.