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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 Number s.


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