Timeline for Generalized Collatz sequences
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Jan 16 at 21:30 | comment | added | Gottfried Helms | Perhaps there is something with the wieferich prime $k=3511$ wich is $k \equiv 3 \pmod 4$. In R. Crandall's article of 1978 he discusses in short a specific property using the other wieferich prime $j=1093$ (but which is $j \equiv 1 \pmod 4$ and thus uninteresting for your question). It seems he says, that necessarily there must be divergent trajectories (but I never got his idea and analysis properly, sorry). Because he uses the specific property of being "wieferich" it may extend as well to $j$ but which he didn't discuss. So - perhaps that might fit your question here. | |
| Oct 6, 2020 at 8:19 | vote | accept | Dominic van der Zypen | ||
| Oct 6, 2020 at 8:19 | comment | added | Dominic van der Zypen | Right, sorry, I missed it. Thanks for your answer and your effort! | |
| Oct 5, 2020 at 22:03 | comment | added | zeraoulia rafik | @DominicvanderZypen, Why you didn't accept my answer if it convincing ? | |
| Sep 28, 2020 at 16:01 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Sep 28, 2020 at 15:50 | comment | added | Dominic van der Zypen | Right @wojowu, sorry for neglecting this. Will amend it. | |
| Sep 28, 2020 at 8:16 | comment | added | Wojowu | I see you have corrected the definition but not the erroneous claim about $k=4a+1$. Do you happen to know if any of that claim is salvageable? | |
| Sep 27, 2020 at 22:25 | comment | added | zeraoulia rafik | @DominicvanderZypen you have claimed in your first par of your question that the smallest known value of $a$ satisfying this would be of interest , could u pleas add some explanation about this point ? | |
| Sep 27, 2020 at 21:46 | history | became hot network question | |||
| Sep 27, 2020 at 19:39 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
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| Sep 27, 2020 at 19:35 | comment | added | Dominic van der Zypen | That's right @wojowu, will correct! And thanks everyone for the remarks for $n=5$ | |
| Sep 27, 2020 at 14:51 | answer | added | zeraoulia rafik | timeline score: 5 | |
| Sep 27, 2020 at 14:29 | comment | added | Wojowu | See also my question at Math.SE. I don't think there are any known (provably) divergent trajectories in any of your sequences. | |
| Sep 27, 2020 at 14:21 | comment | added | Wojowu | Are you sure you mean $n\mapsto c_k(n-1)$ and not $n\mapsto c_k(Coll_{x,k}(n-1))$? Your claim about $k=4a+1$ is incorrect, since for $k=5$ the sequence starts with $5,26,13,66,33,166,83,416$ which is divisible by $4$. | |
| Sep 27, 2020 at 14:14 | comment | added | Goldstern | Note that $k=4a+1$ is not completely uninteresting. For example, $k=5$ gets you the cycle 13,66,33,166,83,416,208,104,52,26,13, which does not contain 1. | |
| Sep 27, 2020 at 14:09 | comment | added | zeraoulia rafik | I think the answer is negative because it was shown by Terras that for almost all ${N}$ (in the sense of natural density), one has ${\mathrm{Col}_{\min}(N) < N}$ and this was then improved by Allouche and if there is a small a the investigation for it would be beyond current tecknology | |
| Sep 27, 2020 at 13:45 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |