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# examples of Keith numbers

Take the number 47 as it is written in base 10, and start a Fibonacci-like sequence from its digits: 4, 7, 11, 18, 29, 47, …

42, on the other hand, isn’t a Keith number: 4, 2, 6, 8, 14, 22, 36, 58, etc.

For 3-digit numbers, the analogy is to the tribonacci sequence: 1, 9, 7, 17, 33, 57, 107, 197, …

In binary, 2 is a Keith number: 1, 0, 1, 1, 10, … Generalizing, $b$ is a Keith number in base $b$ only if it appears in the Fibonacci sequence, and $b^{x}$ if in the applicable $x$bonacci sequence.

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## Mathematics Subject Classification

11A63*no label found*

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