3n+1问题证明范围的减缩及其叠代数列的构造性质

3n+1 Problem′s Simplifying and Structure Property of {T(n)}(n∈N)

证明了3n+1问题中对数列{T(n)}(n∈N)的讨论,可归结得到{T0(m)}(m≡3(mod6)的情形.利用分类分段法得到了相应奇数列{T0(m)}(m≡3(mod6))的构造性质,同时对3n+1问题直接证明的条件进行了探讨.

We prove that discussing about {T(n)}(n∈N) in 3n+1 problem can be reduced to {T0(m)}(m∈N)(m≡3(mod6)). A structural property of {T0(m)}(m≡3(mod6)) is obtained by classified and segregated segment method,so 3n+1 problem is simplified.