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A combined algorithm is required to select an optimal set of sensors, satisfying the conditions of coverage and connectivity. Since topological changes have significant impact on the coverage quality, there is a need for dynamic coverage maintenance algorithms. In this paper, an energy efficient distributed connected coverage (EEDCC) algorithm and a set of dynamic coverage maintenance (DCM) algorithms have been proposed. EEDCC aims to reduce the energy consumption with a lower communication overhead. The DCM algorithms aid in the tracking of changes in network topology thereby addressing the issues related to dynamic coverage and loss recovery. These algorithms would assist in the adaptive maintenance of the coverage either by migrating sensor node or by updating the radii accordingly. Simulations results show that the EEDCC-DCM algorithms attain significant reduction of energy, with strong connectivity and coverage.