While transformer models exhibit strong capabilities on linguistic tasks, their complex architectures make them difficult to interpret. Recent work has aimed to reverse engineer transformer models into human-readable representations called circuits that implement algorithmic functions. We extend this research by analyzing and comparing circuits for similar sequence continuation tasks, which include increasing sequences of digits, number words, and months. Through the application of circuit analysis techniques, we identify key sub-circuits responsible for detecting sequence members and for predicting the next member in a sequence. Our analysis reveals that semantically related sequences rely on shared circuit subgraphs with analogous roles. Overall, documenting shared computational structures enables better prediction of model behaviors, identification of errors, and safer editing procedures. This mechanistic understanding of transformers is a critical step towards building more robust, aligned, and interpretable language models.