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Results tagged with collatz-conjecture
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user 28104
The Collatz Conjecture, also known as the 3n+1 conjecture, is a famous open problem named after Lothar Collatz.
47
votes
1
answer
2k
views
Transitivity on $\mathbb{N}_0$ -- a 42 problem
Let $r(m)$ denote the residue class $r+m\mathbb{Z}$, where $0 \leq r < m$.
Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$, let the class
transposition $\tau_{r_1(m_1),r_2(m_2)}$ be the permu …
- 19.6k
3
votes
0
answers
174
views
Largest permutation groups without "non-mixing" subgroups
We say that a subgroup of ${\rm Sym}(\mathbb{N})$ has sparse orbit representatives
if it has infinitely many orbits on $\mathbb{N}$, but the set of smallest orbit
representatives has natural density 0 …
- 19.6k
1
vote
1
answer
239
views
Group with 2 orbits on the nonnegative integers -- description of the orbits
Definition: Let $r(m)$ denote the residue class $r+m\mathbb{Z}$,
where $0 \leq r < m$. Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$,
let the class transposition $\tau_{r_1(m_1),r_2(m_2)}$ …
- 19.6k
11
votes
Accepted
Collatz stopping-time and Poisson distribution, and connection to other problems?
As to the observed distribution of total stopping times for integers $n \leq 10^8$,
I think heuristically this can be explained quite well by the obvious stochastic model
(multiply $n$ by $3/2$ or $1/ …
- 19.6k