3N+1猜想的超级压缩迭代性质

Some properties of super contraction iteration in 3N+1 conjecture

在3N+1猜想的研究中,运用去偶算子提出了超级压缩迭代概念,建立了超级压缩迭代轨迹序列,与原有的压缩迭代相比大大提高了迭代速度;提出了筛数概念并在此基础上得出了压缩迭代与超级压缩迭代之间的周期(或称圈长)关系,从而得到在超级压缩迭代下一个奇数y的一阶先驱数中4k+3型的奇数不是惟一的结果;给出了超级压缩迭代下的周期数存在的一个必要条件.这些性质与定理的建立对于研究世界著名数论难题3N+1猜想起到简化作用,同时也为3N+1猜想的继续研究提供了新思路.

In researching of 3N＋1 conjecture, by useing operator of dividing even factor, this paper provided the concept of super contraction and series of iteration super contraction iteration, which greatly increased iteration velocity in comparison with former contraction iteration. At the same time,this paper first provided the concept of omission numbers and obtained the cyclic relation between contraction iteration and super contraction iteration, and obtained no unique property about precursor numbers of monadic-order to odd number in super contraction iteration, and to the odd number y of 4k＋3, obtained no unique property about precursor numbers of monadic-order to odd number in super contracion iteration. At last, this paper first provided necessary condition of existence of cyclic numbers in super contraction iteration, which can play active role in cyclic numbers researching of 3N＋1 conjecture. All presented definitions and theories can simplify in researching world well-known problem 3N＋1 conjecture in number theory. This paper also provides new method in 3N＋1 conjecture continuous researching.