Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach

The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achiev...

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Published in:IEEE access Vol. 13; pp. 41210 - 41220
Main Authors: Getachew, Eyob Solomon, Assefa, Beakal Gizachew
Format: Journal Article
Language:English
Published: IEEE 2025
Subjects:
Algorithm optimization
and large-scale verification
Approximation algorithms
bitwise operations
Collatz conjecture
Collatz tree
Complexity theory
computational complexity
Computational efficiency
computational mathematics
Encryption
high-performance algorithms
logarithmic complexity
memoization
Optimization
parallel computing
Probabilistic logic
sequence analysis
stopping time
Testing
Time complexity
Visualization
Watermarking
ISSN:2169-3536, 2169-3536
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Abstract The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achieving significant computational improvements. By leveraging structural patterns in the Collatz tree, the proposed algorithm minimizes redundant operations and optimizes computational steps. Unlike prior methods, it efficiently handles extremely large numbers without requiring advanced techniques such as memoization or parallelization. Experimental evaluations confirm computational efficiency improvements of approximately 28% over state-of-the-art methods. These findings underscore the algorithm's scalability and robustness, providing a foundation for future large-scale verification of the conjecture and potential applications in computational mathematics.
AbstractList The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achieving significant computational improvements. By leveraging structural patterns in the Collatz tree, the proposed algorithm minimizes redundant operations and optimizes computational steps. Unlike prior methods, it efficiently handles extremely large numbers without requiring advanced techniques such as memoization or parallelization. Experimental evaluations confirm computational efficiency improvements of approximately 28% over state-of-the-art methods. These findings underscore the algorithm's scalability and robustness, providing a foundation for future large-scale verification of the conjecture and potential applications in computational mathematics.
Author Getachew, Eyob Solomon
Assefa, Beakal Gizachew
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SubjectTerms Algorithm optimization
and large-scale verification
Approximation algorithms
bitwise operations
Collatz conjecture
Collatz tree
Complexity theory
computational complexity
Computational efficiency
computational mathematics
Encryption
high-performance algorithms
logarithmic complexity
memoization
Optimization
parallel computing
Probabilistic logic
sequence analysis
stopping time
Testing
Time complexity
Visualization
Watermarking
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Title Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach
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