  In this short paper we outline a recipe for the reconstruction of $F(R)$
gravity starting from single field inflationary potentials in the Einstein
frame. For simple potentials one can compute the explicit form of $F(R)$,
whilst for more involved examples one gets a parametric form of $F(R)$. The
$F(R)$ reconstruction algorithm is used to study various examples: power-law
$\phi^n$, exponential and $\alpha$-attractors. In each case it is seen that for
large $R$ (corresponding to large value of inflaton field), $F(R) \sim R^2$.
For the case of $\alpha$-attractors $F(R) \sim R^2$ for all values of inflaton
field (for all values of $R$) as $\alpha\to0$. For generic inflaton potential
$V(\phi)$, it is seen that if $V^\prime/V \to0$ (for some $\phi$) then the
corresponding $F(R) \sim R^2$. We then study $\alpha$-attractors in more detail
using non-perturbative renormalisation group methods to analyse the
reconstructed $F(R)$. It is seen that $\alpha\to0$ is an ultraviolet stable
fixed point of the renormalisation group trajectories.
