All Questions
Tagged with collatz-conjecture reference-request
8 questions
16
votes
3
answers
4k
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Is it known that the Collatz-like sequence with 7n+1 diverges to infinity starting with 7?
In this question I was wondering if the $3$ in the Collatz conjecture is arbitrary, and when I wrote that question I tried to change to $7n+1$ starting with the seed number $7$, the sequence appears ...
- 541
1
vote
0
answers
158
views
A question and reference about Bombieri's article continued fraction of algebraic numbers
Above the Comments in the article continued fraction of algebraic numbers, there are some words on the unboundedness/cycle of coefficients of continued fraction of algebraic numbers "Thus, ...
- 3,084
2
votes
1
answer
1k
views
Reference on the Collatz conjecture [closed]
I'm just looking for references in the literature for some observations I made for fun about the Collatz conjecture.
The Collatz conjecture states that any positive integer $n$ can eventually be ...
- 179
4
votes
0
answers
504
views
Collatz conjecture and a diophantine equation
Let $M \ge 2$. Inspired by the Collatz iteration / algorithm ($M=2$), I tried the following function:
$$C_M(n) = n/M, \text{ if } n \equiv 0 \mod M, \text{ otherwise } (M+1)n+\{(M-n) \mod M \}$$
We ...
- 3,054
9
votes
1
answer
942
views
Residue class sufficiency sets for the Collatz conjecture
I have recently managed to show a sequence of sufficiency sets for the Collatz conjecture whose natural density approaches 0 (the set theoretic limit approaches the set $\{1\}$). It is an extension of ...
- 2,275
-1
votes
1
answer
376
views
Collatz property implying infinite "fall below" trajectories, is it known?
(this was discovered analyzing Collatz empirically.)
a key aspect of resolving Collatz involves looking at the number of iterations for trajectories to "fall below" the initial value.
consider a ...
- 529
5
votes
2
answers
2k
views
3n+1 problem and cycles
Just to make sure I am up to date with this problem. I know (or I think I do) that it is not yet proven that there are no non-trivial cycles for the collatz sequence (please correct me if I am wrong). ...
- 2,275
10
votes
2
answers
4k
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Larger cycle than 4, 2, 1 in Collatz iteration?
(Here I discuss the Collatz problem only for positive integers.)
It is possible, by computation, to find all cycles in the Collatz iteration of a fixed length.
It is clear that an increase must be ...
- 3,645