On a problem of Schweiger concerning normal numbers

Cor Kraaikamp, Hitoshi Nakada

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 Tm=Sn. 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 languageEnglish
Pages (from-to)330-340
Number of pages11
JournalJournal of Number Theory
Issue number2
Publication statusPublished - 2001 Feb
Externally publishedYes


  • Normal numbers

ASJC Scopus subject areas

  • Algebra and Number Theory


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