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A Conjecture Equivalent to the Collatz Conjecture

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 نشر من قبل Ashish Tiwari
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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 تأليف Ashish Tiwari




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We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.



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Lothar Collatz had proposed in 1937 a conjecture in number theory called Collatz conjecture. Till today there is no evidence of proving or disproving the conjecture. In this paper, we propose an algorithmic approach for verification of the Collatz co njecture based on bit representation of integers. The scheme neither encounters any cycles in the so called Collatz sequence and nor the sequence grows indefinitely. Experimental results show that the Collatz sequence starting at the given integer , oscillates for finite number of times, never exceeds 1.7 times (scaling factor) size of the starting integer and finally reaches the value 1. The experimental results show strong evidence that conjecture is correct and paves a way for theoretical proof.
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