= Solution
For positive <wavenumber>, the condition gives $\omega=Ck^{-n/2}$ on the positive-<frequency> branch. The <group velocity> and <phase velocity> are consequently related by
$$
v_g=\frac{d\omega}{dk}=-\frac n2\frac\omega k=-\frac n2v_p.
$$
The required positive ratio $v_g/v_p=2$ gives $\boxed{n=-4}$. Isotropy makes these <velocities> parallel to the wave vector when this coefficient is positive. Identifying <group velocity> with <energy> transport assumes the usual lossless narrowband <wave packet> regime.
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