  A reconstruction of modified gravity is proposed by establishing a
correspondence between the effective density of the modified gravity and the
holographic density. The non-homogeneous term in the modified Friedmann
equation, generated by the vacuum (holographic) energy density, lead to
reconstructed models that contain explicitly, as part of the solution, the
Einstein-Hilbert term. It was shown that the $\Lambda$CDM-type cosmic histories
allow the general relativity Lagrangian with cosmological constant as a
particular reconstructed solution. The Starobinsky term appears in some
reconstructed solutions, and an approximate reconstruction of the Chaplygin gas
cosmology was performed in terms of elementary functions of curvature.
