Eulerconstant like
Public  04/28/17  13xp  Math  30.6% 
What is $ \sum\limits_{0 \lt 1+4\times k \le n} \frac{1}{1+4\times k}  \frac{\log(n)}{4} \textrm{ when }n \to \infty$
Give your answer with 30 digits after the decimal point.
[My timing: instant]
Hint: there is a closed form.
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