We consider mutual discovery of asynchronous wireless transceivers with a fixed activity ratio. On-off activity patterns are slotted, and repeat in discovery frames. For discovery it has to be guaranteed that the activity patterns of two transceivers are not overlapping. We design necklace codes determining activity patterns to guarantee discovery within a discovery frame, so that two asynchronous transceivers always have non-overlapping activity patterns. The number of distinct patterns is analyzed as a function of discovery frame length, and on-off activity ratio. As an application example, we consider the discovery problem for vehicle-to-vehicle communication. To guarantee discovery of far-away vehicles, discovery sequences providing processing gain, and necklace coded activity patterns are needed. We find that billions of discovery code identities can be provided with a repetition frequency that is high enough to guarantee a missed discovery probability less than 10⁻⁶.