# 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.

Title | examples of Keith numbers |
---|---|

Canonical name | ExamplesOfKeithNumbers |

Date of creation | 2013-03-22 16:01:35 |

Last modified on | 2013-03-22 16:01:35 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 6 |

Author | PrimeFan (13766) |

Entry type | Example |

Classification | msc 11A63 |