Keith number

In recreational mathematics, a Keith number or repfigit number (short for repetitive Fibonacci-like digit) is a natural number ${\displaystyle n}$ in a given number base ${\displaystyle b}$ with ${\displaystyle k}$ digits such that when a sequence is created such that the first ${\displaystyle k}$ terms are the ${\displaystyle k}$ digits of ${\displaystyle n}$ and each subsequent term is the sum of the previous ${\displaystyle k}$ terms, ${\displaystyle n}$ is part of the sequence. Keith numbers were introduced by Mike Keith in 1987.^[1] They are computationally very challenging to find, with only about 100 known.