10 Conclusion

By interpreting Turing machine tapes as binary numbers, we have defined a class of integer sequences—binary step sequences—that directly reflect the locality and mechanical constraints of computation. We have provided a complete and rigorous characterization for all finite sequences of this type. The central open problem remains the characterization of TM-generable infinite sequences, which we conjecture is a proper subset of all infinite binary step sequences. We hope this work opens new avenues for analyzing computational processes through the lens of number theory, suggesting a deeper structure underlying the seemingly unpredictable behavior of Turing machines.

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