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We design an efficient sensing order selection strategy for a distributed cognitive radio (CR) network, where two or more autonomous CRs sense the channels sequentially (in some sensing order) for spectrum opportunities. We are particularly interested in the case where CRs with false alarms autonomously select the sensing orders in which they visit channels, without coordination from a centralized entity. We propose an adaptive persistent sensing order selection strategy and show that this strategy converges and reduces the likelihood of collisions among the autonomous CRs as compared to a random selection of sensing orders. We also show that, when the number of CRs is less than or equal to the number of channels, the proposed strategy enables the CRs to converge to collision-free channel sensing orders. The proposed adaptive persistent strategy also reduces the expected time of arrival at collision-free sensing orders as compared to the randomize after every collision strategy, in which a CR, upon colliding, randomly selects a new sensing order.