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In mathematics, a 'Keith number' or 'repfigit number' (short for 'rep'etitive 'F'ibonacci-like d'igit') is an integer ''N''>9 that appears as a term in a linear recurrence relation with initial terms based on its own digits. Given an ''n''-digit number
$N=sum\_\{i=0\}^\{n-1\}\; 10^i\; \{d\_i\},$
a sequence $S\_N$ is formed with initial terms $d\_\{n-1\},\; d\_\{n-2\},ldots,\; d\_1,\; d\_0$ and with a general term produced as the sum of the previous ''n'' terms. If the number ''N'' appears in the sequence $S\_N$, then ''N'' is said to be a Keith number.
For example, taking 197 in such a way creates the sequence $1,\; 9,\; 7,\; 17,\; 33,\; 57,\; 107,\; 197,\; ldots$. The first few Keith numbers are:
14, 19, 28, 47, 61, 75, 197, 742, 1104, 1537, 2208, 2580, 3684, 4788, 7385, 7647, 7909
Whether or not there are infinitely many Keith numbers is currently a matter of speculation. There are only 71 Keith numbers below 10¹⁹, making them much rarer than prime numbers.
Mike Keith is a mathematician who published a paper on these numbers titled "Repfigit Numbers" in a 1987 issue of the ''Journal of Recreational Mathematics''.

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★ Keith Number - From MathWorld