Sierpiński's constant
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The Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is by limiting the expression:
![K=\lim_{n \to \infty}\left[\sum_{k=1}^{n}{r_2(k)\over k} - \pi\ln n\right]](../../../math/0/5/c/05c1914b8986cf6395c3fb4a5d713c89.png)
where r2(k) is a number of representations of k as a sum of the form a2 + b2 for natural a and b.
Its value is approximately:
- K ≈ 2.58498 17595 79253 21706 58936
[edit] See also
[edit] External links
- http://www.scenta.co.uk/tcaep/science/constant/details/sierpinskisconstant.xml
- http://pi.lacim.uqam.ca/piDATA/sierpinski.txt - Sierpiński's constant up to 2000th decimal digit.
- Eric W. Weisstein, Sierpinski Constant at MathWorld.
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