Timeline for Fibonacci sequence inversion
Current License: CC BY-SA 2.5
16 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2023 at 21:30 | comment | added | Тyma Gaidash | If one wants, an answer for $n\in\Bbb C$ and all branches can be written in closed form using series solution for general trinomial | |
| Mar 10, 2017 at 9:42 | history | edited | CommunityBot |
replaced http://upload.wikimedia.org/ with https://upload.wikimedia.org/
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| Jan 8, 2012 at 12:08 | answer | added | joro | timeline score: 2 | |
| Mar 10, 2011 at 15:14 | vote | accept | Hernán Eche | ||
| Oct 4, 2010 at 16:06 | answer | added | resolvent | timeline score: 1 | |
| Sep 18, 2010 at 0:47 | answer | added | Victor Miller | timeline score: 9 | |
| Sep 17, 2010 at 20:21 | comment | added | Sergei Ivanov | The logarithm seems inevitable, but you can get rid of the floor function at the expense of some square roots. Just observe that $5F_n^2-2=\varphi^{2n}+\varphi^{-2n}$ and solve a quadratic equation in $\varphi^{2n}$. | |
| Sep 17, 2010 at 20:11 | comment | added | Mikola | If a logarithm is distasteful, then you could also just iteratively compute the Fourier series until you find a number which is either greater than or equal to the number you are looking for. By doing this, you would ultimately find the index you want in time proportional to its location in the sequence. Since the Fourier series terms grow exponentially, this algorithm would be polynomial on the size of the input number (in bits), and so it isn't really that inefficient. | |
| Sep 17, 2010 at 19:51 | history | edited | Tony Huynh | CC BY-SA 2.5 |
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| Sep 17, 2010 at 19:38 | answer | added | Mark Bennet | timeline score: 1 | |
| Sep 17, 2010 at 18:57 | answer | added | Michael Lugo | timeline score: 2 | |
| Sep 17, 2010 at 18:43 | comment | added | Michael Lugo | There's a sense in which the logarithm seems inelegant here, I think. | |
| Sep 17, 2010 at 18:20 | history | edited | Charles Matthews | CC BY-SA 2.5 |
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| Sep 17, 2010 at 18:08 | answer | added | Charles Matthews | timeline score: 3 | |
| Sep 17, 2010 at 18:02 | comment | added | Qiaochu Yuan | What's wrong with the logarithm? | |
| Sep 17, 2010 at 17:19 | history | asked | Hernán Eche | CC BY-SA 2.5 |