156 reputation
17
bio website
location Chennai, India
age 19
visits member for 2 years
seen Jun 5 '13 at 11:07

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.


Aug
26
comment 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.
Jul
30
comment 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.
Jul
30
comment 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.
Jul
29
comment 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.
Jul
29
comment A prime number pattern
Link here. Thank you @Gerry Myerson!
Jul
29
comment 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.
Jul
29
comment A prime number pattern
@irrelephant: Sorry about that, fixed it. Thanks
Jul
29
comment 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
Jul
29
comment 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)