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Power consumption on mobile phones is a painful obstacle towards adoption of continuous sensing driven applications, e.g., continuously inferring individual's locomotive activities (such as 'sit', 'stand' or 'walk') using the embedded accelerometer sensor. To reduce the energy overhead of such continuous activity sensing, we first investigate how the choice of accelerometer sampling frequency & classification features affects, separately for each activity, the "energy overhead" vs. "classification accuracy" tradeoff. We find that such tradeoff is activity specific. Based on this finding, we introduce an activity-sensitive strategy (dubbed "A3R" - Adaptive Accelerometer-based Activity Recognition) for continuous activity recognition, where the choice of both the accelerometer sampling frequency and the classification features are adapted in real-time, as an individual performs daily lifestyle-based activities. We evaluate the performance of A3R using longitudinal, multi-day observations of continuous activity traces. We also implement A3R for the Android platform and carry out evaluation of energy savings. We show that our strategy can achieve an energy savings of 50% under ideal conditions. For users running the A3R application on their Android phones, we achieve an overall energy savings of 20-25%.