I am writing this memo to summarize our collaborative work on two key aspects related to the mysterious sequence (MS): compressing the 65536 terms and observing the stabilization of MS terms 1 to 65536.
- Compressing the 65536 Terms:
Our objective was to compress the 65536 terms of the MS sequence to minimize storage requirements while preserving the sequence’s essential information. We explored various approaches and eventually settled on a method that involved packing the sequence’s bits sequentially. By using C code, we successfully generated a binary representation of the unpacked bits and saved the output to a file named “bin2exp20.” Subsequently, you compressed the file using WinRAR with the “best” compression settings, resulting in a compressed file size of 7336 bytes. - Stabilization of MS Terms 1 to 65536:
To examine the behavior of the MS sequence, we simulated the first 65536 terms of the sequence and observed any patterns or repetitions. Through our analysis, we observed that certain bits of the MS sequence exhibited periodicity, with bit 3 repeating every 16 terms. Additionally, we noticed other regularities and conjectured that bit k of the MS sequence appeared to be a function of n % (2^k), where n is the term index.
In summary, our collaborative work led to the successful compression of the 65536 terms of the MS sequence, reducing the storage requirements significantly. Additionally, our observations and conjectures about the stabilization and regularities in the MS sequence provide valuable insights into its behavior and potential underlying patterns.
Please feel free to review and provide any additional details or corrections to this summary. If you have any further questions or if there’s any other aspect you’d like to explore, please let me know.
Thank you for your collaboration and contributions to this project.
