查看“︁斯托納姆數”︁的源代码

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'''斯托納姆數'''（{{lang|en|'''Stoneham numbers'''}}）是一種特別的[[實數]]，得名自數學家李查·斯托納姆（Richard G. Stoneham, 1920–1996）。對於[[互質]]且大於1的整數''b''和''c''，可以定義斯托納姆數&alpha;<sub>''b'',''c''</sub> 如下：

:<math>\alpha_{b,c} = \sum_{n=c^k>1} \frac{1}{b^nn} = \sum_{k=1}^\infty \frac{1}{b^{c^k}c^k}</math>

斯托納姆在1973年證明只要''c''為奇[[質數]]，而''b''是''c''<sup>2</sup>的[[原根]]，則斯托納姆數是以b為底的[[正規數]]。

== 參考資料 ==
{{reflist}}
*{{cite book|last=Bugeaud|first=Yann|title=Distribution modulo one and Diophantine approximation|series=Cambridge Tracts in Mathematics|volume=193|location=Cambridge|publisher=[[Cambridge University Press]]|year=2012|isbn=978-0-521-11169-0|zbl=1260.11001}}
*{{cite journal | zbl=0276.10028 | last=Stoneham | first=R.G. | title=On absolute $(j,ε)$-normality in the rational fractions with applications to normal numbers | journal=[[Acta Arithmetica]] | volume=22 | pages=277-286 | year=1973 }}
*{{cite journal | zbl=0276.10029 | last=Stoneham | first=R.G. | title=On the uniform ε-distribution of residues within the periods of rational fractions with applications to normal numbers | journal=[[Acta Arithmetica]] | volume=22 | pages=371-389 | year=1973 }}

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[[Category:数论]]
[[Category:實數]]