In mathematics, the Lambert-W function, also called the omega function or product logarithm, is a set of functions, namely the branches of the inverse relation of the function f(z) = zez where ez is the exponential function and z is any complex number. In other words
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As the title says, I would like to launch a community project for
proving that the series $$\sum_{n\geq 1}\frac{\sin(2^n)}{n}$$ is
convergent.
An extensive list of considerations follows. The first fact is that the inequality
$$ \sum_{n=1}^{N}\sin(2^n)\ll N^{1-\varepsilon}\qquad\text{or}...
