The smallest value of $k$, for which both the roots of the equation $$x^{2}-8kx+16\left(k^{2}-k+1\right)=0$$ are real, distinct and have values at least 4, is
The smallest value of $k$, for which both the roots of the equation
$$x^{2}-8kx+16\left(k^{2}-k+1\right)=0$$
are real, distinct and have values at least 4, is