# parasitic number

Given a base $b$ integer $n$ with $k$ digits ${d}_{1},\mathrm{\dots},{d}_{k}$ (with ${d}_{1}$ being the least significant digit), and an integer $$, if it is the case that

$$m(\sum _{i=1}^{k}{d}_{i}{b}^{i-1})={d}_{1}{b}^{k-1}+(\sum _{i=2}^{k}{d}_{i}{b}^{i-2}),$$ |

then $n$ is called an $m$-parasitic number or $m$-left-transposable number.

If one takes an $m$-parasitic number, concatenates copies of its digits in order whatever number of times one wants, the resulting new number will also be $m$-parasitic.

Title | parasitic number |
---|---|

Canonical name | ParasiticNumber |

Date of creation | 2013-03-22 16:22:17 |

Last modified on | 2013-03-22 16:22:17 |

Owner | CompositeFan (12809) |

Last modified by | CompositeFan (12809) |

Numerical id | 4 |

Author | CompositeFan (12809) |

Entry type | Definition |

Classification | msc 11A63 |

Synonym | left-transposable integer |