Sierpiński's constant

From Freepedia

The Sierpiński's constant is a mathematical constant usually denoted as K. One way of defining it is by limiting the expression:

<math>K=\lim_{n \to \infty}\left[\sum_{k=1}^{n}{r_2(k)\over k} - \pi\ln n\right]</math>

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

See also

• Wacław Sierpiński

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.