Timeline for 3-adic valuation of a sum involving binomial coefficients
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| May 6, 2017 at 8:36 | vote | accept | Jeffrey Shallit | ||
| May 6, 2017 at 6:30 | answer | added | T. Amdeberhan | timeline score: 11 | |
| May 6, 2017 at 0:55 | answer | added | Jeffrey Shallit | timeline score: 7 | |
| May 5, 2017 at 15:30 | comment | added | Jeffrey Shallit | Perhaps the right generalization is that the sequence $f(n) = \nu_p(P_n (p))$, for $P_n$ the $n$'th Legendre polynomial, and $p$ is a prime $\geq 3$, is a $p$-regular sequence (in the sense of my paper with Allouche). I just tried it for $p = 5$ and it seems to satisfy relations like $f(5n+2) = f(5n)$, etc. | |
| May 5, 2017 at 15:13 | comment | added | Jeffrey Shallit | I have no results for anything other than 3. Maybe that is because of Alekseyev's observation? I don't know. | |
| May 5, 2017 at 15:06 | comment | added | Igor Rivin | Out of curiosity, is there anything special about $3?$ Do you have results for any other prime (even or otherwise)? | |
| May 5, 2017 at 13:39 | comment | added | Max Alekseyev | It's worth to mention that the $a(n)$ form oeis.org/A001850 with tons of useful info and references. E.g., "$a(n)=P_n(3)$, where $P_n$ is $n$-th Legendre polynomial" sounds particularly relevant. | |
| May 5, 2017 at 13:32 | history | edited | Joe Silverman | CC BY-SA 3.0 |
Improved formatting
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| May 5, 2017 at 12:22 | comment | added | YCor | It was my guess after 30s rereading to find where is the question, but it's better now that it's explicit. Also I wasn't 100% sure that "a more elegant proof by Zagier" does not refer to your conjecture. | |
| May 5, 2017 at 12:21 | history | edited | Jeffrey Shallit | CC BY-SA 3.0 |
added 28 characters in body
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| May 5, 2017 at 12:20 | comment | added | Jeffrey Shallit | Really? It's not obvious? I am asking for a proof (or counterexample, if it's false). | |
| May 5, 2017 at 12:20 | comment | added | YCor | What is the question? | |
| May 5, 2017 at 10:40 | history | edited | Jeffrey Shallit |
edited tags
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| May 5, 2017 at 10:28 | history | asked | Jeffrey Shallit | CC BY-SA 3.0 |