A Keith number or repfigit number is an integer, which, in a given base, if its digits are used as the first terms of a numerical sequence like the Fibonacci numbers sequence, the integer itself occurs later on in the sequence. For example, taking 47 in such a way creates the sequence 4, 7, 11, 18, 29, 47... 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.
