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We investigate the corresponding relation between $f(R)$ gravity and aninteracting holographic dark energy. By obtaining conditions needed for someobservational evidence such as, positive acceleration expansion of universe,crossing the phantom divide line and validity of thermodynamics second law inan interacting HDE model and corresponding it with $f(R)$ mode of gravity wefind a viable $f(R)$ model which can explain the present universe. We alsoobtain the explicit evolutionary forms of the corresponding scalar field,potential and scale factor of universe.

Reconstructing f(R) model from Holographic DE: Using the observational evidence