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:

where r2(k) is a number of representations of k as a sum of the form a2 + b2 for natural a and b.

It can be given in closed form as:

where is Gauss's constant and is the Euler-Mascheroni constant.

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