Corpus ID: 117814996

New results on the stopping time behaviour of the Collatz 3x + 1 function

@article{Winkler2015NewRO,
  title={New results on the stopping time behaviour of the Collatz 3x + 1 function},
  author={M. Winkler},
  journal={arXiv: General Mathematics},
  year={2015}
}

M. Winkler

Published 2015

Mathematics

arXiv: General Mathematics

Let $\sigma_n=\lfloor1+n\cdot\log_23\rfloor$. For the Collatz 3x + 1 function exists for each $n\in\mathbb{N}$ a set of different residue classes $(\text{mod}\ 2^{\sigma_n})$ of starting numbers $s$ with finite stopping time $\sigma(s)=\sigma_n$. Let $z_n$ be the number of these residue classes for each $n\geq0$ as listed in the OEIS as A100982. It is conjectured that for each $n\geq4$ the value of $z_n$ is given by the formula \begin{align*} z_n=\frac{(m+n-2)!}{m!\cdot(n-2)!}-\sum_{i=2}^{n-1… CONTINUE READING

View PDF on arXiv

Save to Library

Create Alert

Cite

Launch Research Feed