Timeline for A curious process with positive integers
Current License: CC BY-SA 4.0
22 events
| when toggle format | what | by | license | comment | |
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| S Oct 28, 2018 at 0:00 | history | bounty ended | CommunityBot | ||
| S Oct 28, 2018 at 0:00 | history | notice removed | CommunityBot | ||
| Oct 26, 2018 at 18:41 | answer | added | esg | timeline score: 3 | |
| Oct 21, 2018 at 10:39 | answer | added | Robin Zhang | timeline score: 7 | |
| S Oct 19, 2018 at 22:39 | history | bounty started | Mikhail Tikhomirov | ||
| S Oct 19, 2018 at 22:39 | history | notice added | Mikhail Tikhomirov | Improve details | |
| Oct 16, 2018 at 5:40 | comment | added | მამუკა ჯიბლაძე | Second differences might be simpler... | |
| Oct 16, 2018 at 5:26 | comment | added | Josiah Park | @MikhailTikhomirov It might be interesting to investigate why the even value $k$ diagrams above have loops while the odd ones do not. | |
| Oct 16, 2018 at 5:19 | history | edited | Mikhail Tikhomirov | CC BY-SA 4.0 |
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| Oct 15, 2018 at 2:59 | answer | added | Josiah Park | timeline score: 4 | |
| Oct 14, 2018 at 15:22 | history | edited | Mikhail Tikhomirov | CC BY-SA 4.0 |
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| Oct 14, 2018 at 9:28 | answer | added | LeechLattice | timeline score: 30 | |
| Oct 14, 2018 at 7:47 | history | edited | Mikhail Tikhomirov | CC BY-SA 4.0 |
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| Oct 14, 2018 at 6:01 | comment | added | LeechLattice | It seems that the sequence $Δ_k$ is an automatic sequence in base 3. | |
| Oct 14, 2018 at 4:13 | comment | added | Josiah Park | The density of the largest difference in $\Delta_{k}$ (the largest difference is apparently $k^2$ for $k \geq 3$) seems to be monotonic increasing in $k$ for $k>3$. | |
| Oct 14, 2018 at 3:05 | comment | added | Josiah Park | Another observation is that the difference sets seem very structured in that they consist entirely of consecutive integers. For $k=3,4,5,6,7,8,9,10...$ the first differences in increasing order are $6,13,20,31,42,57,72,91,...$ which are of the form $6,6+7,6+7+7,6+7+7+11,6+7+7+11+11,6+7+7+11+11+15,...$. So beginning with $k=3$ it seems one gets the smallest difference in $\Delta_{k+1}$ by adding to the smallest difference in $\Delta_{k}$ the corresponding number in the sequence $7,7,11,11,15,15,...$. | |
| Oct 14, 2018 at 2:51 | comment | added | Josiah Park | Looking at the differences for increasing $k$ leads to the following observations: For $k=3$ the difference set for $x_{j}$, $\Delta_{3}=\{x_{j+1}-x_{j}\}$, is of size four up to $10000$ steps and consists of the elements $\{6,7,8,9\}$. Similarly for $k=4$ one gets four elements in the difference set. Empirically this type of behavior seems to continue for $k\geq 3$, that is the difference set $\Delta_{k}$ for $k=2j+1,2j+2$ has size $2(j+1)$. | |
| Oct 14, 2018 at 2:41 | history | edited | Mikhail Tikhomirov | CC BY-SA 4.0 |
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| Oct 14, 2018 at 2:34 | history | edited | Mikhail Tikhomirov | CC BY-SA 4.0 |
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| Oct 13, 2018 at 20:56 | comment | added | Mikhail Tikhomirov | @NoamD.Elkies I sure did, but to no avail. | |
| Oct 13, 2018 at 20:55 | comment | added | Noam D. Elkies | did you look for these sequences in the OEIS? | |
| Oct 13, 2018 at 20:46 | history | asked | Mikhail Tikhomirov | CC BY-SA 4.0 |