Keith Number/Examples/754,788,753,590,897

Examples of Keith Number
$754 \, 788 \, 753 \, 590 \, 897$ is a Keith number:
 * $7, 5, 4, 7, 8, 8, 7, 5, 3, 5, 9, 0, 8, 9, 7, \ldots, $

Proof
By definition of Keith number, we create a Fibonacci-like sequence $K$ from $\left({7, 5, 4, 7, 8, 8, 7, 5, 3, 5, 9, 0, 8, 9, 7}\right)$:

Thus $754 \, 788 \, 753 \, 590 \, 897$ occurs in $K$ and the result follows by definition of Keith number.