# Demlo number

Given base $b$, a number of the form ${(\frac{{b}^{n}-1}{b-1})}^{2}$ for $n>0$ (that is, the square of a repunit^{}) is a Demlo number^{}, sometimes called a wonderful Demlo number.

The Demlo numbers for $$ are also palindromic numbers^{}, and specifically of the form

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

that is, the most significant digits are the first $n$ digits of base $b$ in order and the least significant digits are the first $n$ digits of base $b$ backwards.

Title | Demlo number |
---|---|

Canonical name | DemloNumber |

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

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

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A63 |

Synonym | wonderful Demlo number |