Definitions

# Sierpiński's constant

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

$K=lim_\left\{n to infty\right\}left\left[sum_\left\{k=1\right\}^\left\{n\right\}\left\{r_2\left(k\right)over k\right\} - piln nright\right]$

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

• 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.

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