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<p>After having stated several conjectures regarding potential families of normal numbers, we construct various new families of normal numbers using different concepts, in particular the whole set of partitions of the set <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\{0,1,\ldots ,k\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>k</mi> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>, the smallest prime divisor of <i>n</i> which is larger than <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\log n\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>log</mo> <mi>n</mi> </mrow> </math></EquationSource> </InlineEquation>, and finally a certain regroupment of the whole set of primes known as a disjoint classification of primes.</p>

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Various new families of normal numbers

  • 期刊论文

  • 发表日期：

    2026年5月4日

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  • Jean-Marie De Koninck,
  • Imre Kátai

摘要

After having stated several conjectures regarding potential families of normal numbers, we construct various new families of normal numbers using different concepts, in particular the whole set of partitions of the set \(\{0,1,\ldots ,k\}\) { 0 , 1 , … , k } , the smallest prime divisor of n which is larger than \(\log n\) log n , and finally a certain regroupment of the whole set of primes known as a disjoint classification of primes.