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 Arabic numerals, number words, and months. By applying circuit interpretability analysis, we identify a key sub-circuit in both GPT-2 Small and Llama-2-7B 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. Additionally, we show that this sub-circuit has effects on various math-related prompts, such as on intervaled circuits, Spanish number word and months continuation, and natural language word problems. Overall, documenting shared computational structures enables better model behavior predictions, 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.