# digit sum

Given an integer $m$ consisting of $k$ digits ${d}_{1},\mathrm{\dots},{d}_{k}$ in base $b$, let

$$j=\sum _{i=1}^{k}{d}_{i},$$ |

then $j$ is the *digit sum* of $m$. Iterating this operation on the digits of $j$ until $$ gives the digital root or repeated digit sum of $m$. The digit sum and digital root of a number are the same only if the additive persistence of the digital root is 1.

Title | digit sum |
---|---|

Canonical name | DigitSum |

Date of creation | 2013-03-22 16:22:53 |

Last modified on | 2013-03-22 16:22:53 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 5 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11A63 |