Keith number
Given a base integer
where is the least significant digit and is the most significant, construct the sequence , and for ,
If there is an such that , then 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.
References
- 1 M. Keith, “Repfigit Numbers” J. Rec. Math. 19 (1987), 41 - 42.