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 | |
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| Jan 11, 2018 at 10:32 | comment | added | Robert Frost | Ah okay; a cycle having only one division by $4$ or greater. A non-unitary down-step. Containing no more than one integer satisfying $\lvert\cdot\rvert_2\in\{\frac{1}{4},\frac{1}{8}\}$ | |
| Jan 10, 2018 at 20:51 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
added 2397 characters in body
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| Jan 10, 2018 at 20:46 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
added 2397 characters in body
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| Jan 10, 2018 at 20:04 | comment | added | Gottfried Helms | @Robert : "1-cycle" does not mean "only one step" (in the syracuse notation) but "arbitrarily many steps going up only and then arbitrarily many steps going down only arriving at the initial value again". This is often misunderstood (my own first take with this included...) and so I think it is somehow a misnomer. There should a better name be invented sometime... The "1-step-loop" which you describe in your comment is indeed easily disproved (and even the 2-step and 3-step cycle and a couple of such finite-step cycles) see my treatize go.helms-net.de/math/collatz/Collatz061102.pdf | |
| Jan 10, 2018 at 19:04 | comment | added | Robert Frost | Strange that somebody bothered to prove the trivial cycle is the only 1-cycle by such complex means when it's easily shown with basic algebra that $x=1$ is the only positive integer solution to $2^mx=3x+1$ | |
| Mar 10, 2017 at 3:10 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
Updated link to the Simons/deWeger-paper
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| Jun 28, 2011 at 4:21 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
corrected date of reference(Simons,2004)
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| Jun 26, 2011 at 9:25 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
improving explanation
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| Jun 25, 2011 at 5:42 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
added explanation/Code; added 98 characters in body
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| Jun 24, 2011 at 19:48 | history | edited | Gottfried Helms | CC BY-SA 3.0 |
corrected date of reference
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| Jun 24, 2011 at 19:33 | history | answered | Gottfried Helms | CC BY-SA 3.0 |