Timeline for Larger cycle than 4, 2, 1 in Collatz iteration?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 2, 2017 at 11:14 | comment | added | Gottfried Helms | @GerhardPaseman : after I came across that article by R.E.Crandall from 1978 I'm sure this is the one which you remember vaguely. It is an early one (if not the first) which gives a lower bound for the possible length of a cycle depending on its smallest element $a_0$ and puts it in correspondence to a lower bound for $a_\text{emp}$ found by empirical (brute force) determination of trajectory lengthes, where all smaller $a \lt a_\text{emp}$ are known to be not member of a cycle but have a trajectory down to $1$. Crandall had $a_\text{emp} \approx 10^9$ and min. cyclelength $\approx 15000$ | |
| Mar 10, 2017 at 9:15 | comment | added | Gottfried Helms | @JonMarkPerry: allowing rational numbers you can find infinitely many cycles. A short thought on this can even be extracted from the Simons/deWeger-article... | |
| Mar 10, 2017 at 6:36 | comment | added | JMP | interestingly $1/5\to 8/5\to 4/5\to 2/5\to 1/5$ | |
| Jun 25, 2011 at 13:59 | comment | added | TMM | You may want to check arxiv.org/abs/math.NT/0309224 and arxiv.org/abs/math.NT/0608208 for an extensive overview of literature on the Collatz conjecture. One of those lists includes the reference to Simons, De Weger mentioned in the answer below, and there may be other papers relevant to your question listed there as well. | |
| Jun 24, 2011 at 22:04 | answer | added | Alain Valette | timeline score: 5 | |
| Jun 24, 2011 at 19:33 | answer | added | Gottfried Helms | timeline score: 12 | |
| Jun 24, 2011 at 17:49 | comment | added | Gerhard Paseman | Emil, I don't actually recall the paper containing the result, and I have a feeling that I am thinking of a different one. Your citation though is a good one, and I am happy to let that be the example until my memory improves. Thanks for the reference. Gerhard "Thanks For The Memory Substitutes" Paseman, 2011.06.24 | |
| Jun 24, 2011 at 17:19 | comment | added | Emil Jeřábek | What Gerhard means is probably jstor.org/stable/2044308 . | |
| Jun 24, 2011 at 17:15 | comment | added | Emil Jeřábek | See deweger.xs4all.nl/papers/… for up to date results on Collatz cycles. | |
| Jun 24, 2011 at 17:12 | comment | added | Gerhard Paseman | Some of the earliest Internet pages on the Collatz problem refer to work done on cycle lengths. One result had a cycle length over the positive integers as being either the known cycle or else having length be large (more than 100000). A net search/should help you find it. Gerhard "Email Me About System Design" Paseman, 2011.06.24 | |
| Jun 24, 2011 at 17:02 | history | asked | DavidLHarden | CC BY-SA 3.0 |