Generating random number sequences is a popular psychological task often used to measure executive functioning. We explore random generation under “joint cognition” instructions; pairs of participants take turns to compile a shared response sequence. Across three studies, we point to six key findings from this novel format. First, there are both costs and benefits from group performance. Second, repetition avoidance occurs in dyadic as well as individual production settings. Third, individuals modify their choices in a dyadic situation such that the pair becomes the unit of psychological function. Fourth, there is immediate contagion of sequence stereotypy amongst the pairs (i.e., each contributor “owns” their partner’s response). Fifth, dyad effects occur even when participants know their partner is not interacting with them (Experiment 2). Sixth, ironically, directing participants’ efforts away from their shared task responsibility can actually benefit conjoint performance (Experiment 3). These results both constrain models of random generation and illuminate processes of joint cognition.