Given a base $b$ integer $$n = \sum_{i = 1}^k d_ib^{i - 1}$$ where $d_1$ is the least significant digit and $d_k$ is the most significant, construct the sequence $a_1 = d_k, \ldots a_k = d_1$ and for $m > k$ $$a_m = \sum_{i = 1}^k a_{m - i}.$$ If there is an $x$ such that $a_x = n$ then $n$ is a Keith number or repfigit number.

In base 10, the first few Keith numbers below ten thousand are: 14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909 (see A007629 in Sloane's OEIS for a longer listing). 47 is a base 10 Keith number because it is contained the Fibonacci-like recurrence started from its base 10 digits: 4, 7, 11, 18, 29, 47, etc.

Bibliography

1

M. Keith, ``Repfigit Numbers" J. Rec. Math. 19 (1987), 41 - 42.