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| bio | website | |
|---|---|---|
| location | Chennai, India | |
| age | 18 | |
| visits | member for | 10 months |
| seen | Dec 23 '12 at 18:09 | |
| stats | profile views | 12 |
I'm a college student of Computer Science, who likes Number Theory (like you haven't heard that one before!).
You can probably find me online on GMail (furlox.mod@gmail.com) but I wouldn't know why you'd want to do that. I have a thing for four-leggeds, too.
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Aug 26 |
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Primality using $\Gamma(x)$ @Qiaochu Yuan My motive was not Wilson related so much as exploring the Gamma function, being new to it and all. Perhaps 'primality' is an unsuitable term? To Alex, I'll try to be careful =P $a+bi$ where $b$ is non-zero. |
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Jul 30 |
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A prime number pattern Of course, it would also have to happen that the only $1s$ I have encountered in odd number chains correspond to $Z_t$ values, which end the sequence. If this is the only place $1s$ might occur (for odd numbers), the conjecture would fall to induction. |
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Jul 30 |
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A prime number pattern My real bad. That aside, even numbers only get $Z_t\in\{-1,0,1\}$ while odd numbers have $\{0,1,2\}$. Let us assume above observation is true till $2n+1$. Then, we can prove if $2n+1$ never reaches $1$, it will not reach $-1$. Follows from the fact that $2n$ would have the same chain as $2n+1$, but for a displacement of $1$ in values. Hence, at the terminus, $Z_t({2n})$ would displace to $2$ (from $-1$) instead of $-2$. This won't work for for any odd number reaching $1$ in the middle of the sequence, of course. |
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Jul 29 |
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A prime number pattern An elementary result that would follow if odd numbers don't have $−1$ as a terminal is that there always exists a prime between $p_2n+1$ and $−1+\sum_{i=1}^{{2n+}1}p_i$ where $p_n$ is the $n-th$ prime. For example, $-1 + 2 + 3 + 5 = 9$, if there is no prime $p$ such that $5<p<9$ then we have a contradiction. |
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Jul 29 |
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A prime number pattern Link here. Thank you @Gerry Myerson! |
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Jul 29 |
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A prime number pattern Finding numbers for which terminal values are $-1$ still hasn't landed me an odd number. This strongly points towards there being a poof. edit: Read @alex.jordan's explanation, much better than what I posted. |
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Jul 29 |
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A prime number pattern @irrelephant: Sorry about that, fixed it. Thanks |
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Jul 29 |
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A prime number pattern I can't post to OEIS, its unlisted there. Maybe someone might help? Here are some lists filtered by primality. Z=0, Z=1, Z=2 |
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Jul 29 |
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A prime number pattern @alex.jordan Yes. For every other odd prime from 3, the cycle seems to reach 1. However, by removing the is-prime constraint, we also get numbers like 8,14,20,25,27,30,33,35... (for Z=1) |
