What question did this study set out to answer?

This paper aims to analyze the algebraic properties of parameter k to understand its impact on the 3n+1 conjecture's convergence.

April 28, 2026Open Access

关于3n+1猜想收敛性的代数结构分析手稿: Algebraic Structure Analysis Manuscript on the Convergence of the 3n+1 Conjecture

Key Points

This paper aims to analyze the algebraic properties of parameter k to understand its impact on the 3n+1 conjecture's convergence.
Analyzed the odd general term formula n=4k-1
Constructed an iteration model based on energy conservation
Investigated the distribution of factor 2 in parameter k
Proposed that numerical growth is limited by the factor 2 stock in k
Identified a dissipative trend in factor 2 during iterations
Provided a new theoretical explanation for the global convergence of the sequence

Abstract

摘要(Abstract) 中文摘要:本文旨在通过分析奇数通项公式 n=4k-1 中参数 k 的代数性质,特别是因子2的分布规律,构建一种基于“能量守恒”的迭代模型。本文提出:序列中的数值增长受限于 k 中因子2的存量,且该存量在迭代中呈现耗散趋势,从而为序列的全局收敛性提供了新的理论解释。 English Abstract:This paper aims to construct an iteration model based on "energy conservation" by analyzing the algebraic properties of parameter k in the odd general term formula n=4k-1, especially the distribution law of factor 2. This paper proposes that the numerical growth in the sequence is limited by the stock of factor 2 in k, and the stock shows a dissipative trend in the iteration, thus providing a new theoretical explanation for the global convergence of the sequence.

关于3n+1猜想收敛性的代数结构分析手稿: Algebraic Structure Analysis Manuscript on the Convergence of the 3n+1 Conjecture

Key Points

Abstract

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