Keith Number/Examples/129,572,008

Examples of Keith Number
$129 \, 572 \, 008$ is a Keith number:
 * $1, 2, 9, 5, 7, 2, 0, 0, 8, \ldots, 32 \, 456 \, 930, 64 \, 849 \, 899, 129 \, 572 \, 008, \ldots$

Proof
By definition of Keith number, we create a Fibonacci-like sequence $K$ from $\left({1, 2, 9, 5, 7, 2, 0, 0, 8}\right)$:

Thus $129 \, 572 \, 008$ occurs in $K$ and the result follows by definition of Keith number.