### Abstract

Let T and S be two number theoretical transformations on the n-dimensional unit cube B, and write T∼S if there exist positive integers m and n such that T^{m}=S^{n}. F. Schweiger showed in [1969, J. Number Theory1, 390-397] that T∼S implies that every T-normal number x is S-normal. Furthermore, he conjectured that T≁S implies that not all T-normal x are S-normal. In this note two counterexamples to this conjecture are given.

Original language | English |
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Pages (from-to) | 330-340 |

Number of pages | 11 |

Journal | Journal of Number Theory |

Volume | 86 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2001 Feb 1 |

### Keywords

- Normal numbers

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Kraaikamp, C., & Nakada, H. (2001). On a problem of Schweiger concerning normal numbers.

*Journal of Number Theory*,*86*(2), 330-340. https://doi.org/10.1006/jnth.2000.2554