Sierpiński's constant

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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]

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

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