examples of Keith numbers

Take the number 47 as it is written in base 10, and start a Fibonacci-like sequence from its digits: 4, 7, 11, 18, 29, 47, …

42, on the other hand, isn’t a Keith number: 4, 2, 6, 8, 14, 22, 36, 58, etc.

For 3-digit numbers, the analogy is to the tribonacci sequence: 1, 9, 7, 17, 33, 57, 107, 197, …

In binary, 2 is a Keith number: 1, 0, 1, 1, 10, … Generalizing, $b$ is a Keith number in base $b$ only if it appears in the Fibonacci sequence, and $b^x$ if in the applicable $x$bonacci sequence.