2021/03/03 by Ramachandra Bhat, Bhat, Ramachandra
Mathematics · Social Sciences · #11Bxx #Academic integrity and plagiarism #Benford’s Law and Fraud Detection #FOS: Mathematics #General Mathematics (math.GM)
paper · pdf · doi:10.48550/arxiv.2103.03100
openalex publication_date 2021/03/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
As Collatz conjecture is still to be proved, a method to arrive at the\ncomplete proof is explored here. Conceptually, the process relies on the\npre-proven sequence data and the method follows the confirmation of the\nconvergence of the Collatz sequence for all the natural numbers in a sequential\nforward manner (ascending order of n). Hence, all the numbers less than n have\nbeen proved to converge before beginning to prove the convergence of the\nsequence for the number n.\n Initially, the the nature of problem was explored and explained the reason\nfor some of the remarkable properties. Then, the pattern analysis of a first\nfew sequences data led to the concept of pre-proven sequence. Then, the origin\nof quartets and subsequently, the octet patterns are described. The "Even-Odd"\ncombinations and the concept of (8*v + c) gave a clear picture for the overall\nprocess of evaluation for the convergence. Then onwards, individual set of\nnumbers are analyzed and the convergence confirmations are arrived at. The\nprocess of computing involves the concept of combing. Finally, the compilation\nof all the sets together would give the completion of the proof. Here, the\nprocedure for the computation is presented with example and the current status\nof computation (>99 % completed) while the laborious computation is in\nprogress (for the remaining < 1 %). It is expected that the length of the PSO\nnumber list is finite and all the numbers would converge.\n