Natural numbers that can be expressed as the product of two and three consecutive natural numbers Looking for natural numbers larger than 210 which can be expressed as the product of two continuous natural numbers or the product of three continuous natural numbers at the same time.  $6 = 1 \cdot 2 \cdot 3 = 2 \cdot 3$ $210 = 5 \cdot 6 \cdot 7 = 14 \cdot 15$  I have made a program to find that numbers smaller than $1000000000$, only to find $6$ and $210$. Are there any other ones?
How to prove there are no more positive integers that are products of 2 and 3 consecutive numbers? $6$ and $210$ share the property that both are the products of both two and three consecutive numbers. $6$ is $2\times3$ and $1\times2\times3$ and $210$ is $14\times15$ and $5\times6\times7$. It was easy enough to write a program to search for more numbers with this property, I found that there were no more up to at least $1{,}000{,}000{,}000{,}000$ ($1$ Trillion). But it is beyond me to prove that there are either no more numbers like this or to find the next one. Any ideas?
How do I disable X at boot time so that the system boots in text mode? How can I disable a USB port in Windows XP to make it available only for smart phone battery charging?   I don’t want the users to be able to see the USB drive in My Computer, and the USB device should stay disabled in Device Manager.   Is there any way to accomplish this? Best method for short time-series I have a question related to modeling short time-series. It is not a question , but how. What method would you recommend for modeling (very) short time-series (say of length $T \leq 20$)? By "best" I mean here the most robust one, that is the least prone to errors due the fact of limited numbers of observations. With short series single observations could influence the forecast, so the method should provide a cautious estimate of errors and possible variability connected to the forecast. I am generally interested in univariate time-series but it would be also interesting to know about other methods. Interesting tab on StackOverflow One day I directed to SO and was met with the awesome Interesting page, which I really like. But when I travel away from it, I have to re-enter the query string to get it back. Is there a plan to make this tab visible so I can click to it anytime? Difference between generalized linear models & generalized linear mixed models I am wondering what the differences are between mixed and unmixed GLMs. For instance, in SPSS the drop down menu allows users to fit either:   analyze-&gt; generalized linear models-&gt; generalized linear models &amp; analyze-&gt; mixed models-&gt; generalized linear     Do they deal with missing values differently?    My dependent variable is binary and I have several categorical and continuous independent variables. Looking for a sci-fi movie in which a human astronaut befriends an alien on a reddish planet This probably wasn't a blockbuster back in its time as I remember the special effects didn't seem all that bombastic, but I do remember a few details.  A human astronaut lands (or crash-lands) on a prominently reddish planet. It might have been Mars, thought it might not have been. I think the atmosphere on said planet was humanly breathable (as in the astronaut does not wear his helmet).  This human astronaut needs to survive. He spots a humanoid alien, apparently also having crash-landed or otherwise in need of survival. He sees this alien consume some sort of greenish orb, apparently for nourishment. He sneaks up to the alien (or the alien craft) in an attempt to grab some of those greenish orbs. I don't remember whether he succeeds, but he does get beaten up by the alien.  The next bit of detail I remember was the human astronaut constructing some sort of shelter to protect both him and the alien from... meteor showers? The human astronaut piles up some rocks to build a hut while the alien, apparently having learned a few English words, says "shiiiiit" and "no solid". The human astronaut asks, incredulous, "No solid?" and punches the hut he just build. "See? Solid!" he proclaims, while the hut collapses a few seconds later. The alien laughs.  Later on the human astronaut is either caught by or accidentally fell into some sort of mouth-in-the-sand creature. He is saved by the alien in the process (or was it the alien who fell into the mouth-creature and was saved by the human astronaut). They witness the mouth-creature spitting out a turtle-like shell (from another local wildlife) of some sort. The human astronaut observes, and I paraphrase, "This stuff must be so tough that even [the mouth-creature] cannot digest it!" 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What tips should the user know about when dealing with a PPA?. difference between accuracy and Rand index (R) I'm very confused, when I read on the wikipedia "From a mathematical standpoint, Rand index is related to the accuracy, but is applicable even when class labels are not used."   and   But when I use in R the rand.index function from fossil package and the Accuracy function from MLmetrics it doesn't give the same answer  &gt; Accuracy(predicted, real) [1] 0.8266667  &gt; rand.index(predicted,real) [1] 0.7114989  Please can someone explain to me the difference between these two and which one should I use?  NB:I use the k-medoids clustering algorithm (function pam from cluster package) Fast way to find period-n points of a tent map? I need to find a period-3 orbit for a tent map defined by $$T(x)=\begin{cases}2x &amp; 0\le x\le0.5 \\[2ex] 2-2x &amp;0.5 &lt; x \le 1 \end{cases}$$  So, what is a fast and efficient way of finding it? I only know how to do it by guessing-and-checking. For example, I picked a random point, $x = \frac{2}{7}$ and found that $$T\left(\frac{2}{7}\right)=\frac{4}{7}\\[4ex]T\left(\frac{4}{7}\right)=\frac{6}{7}\\[4ex]T\left(\frac{6}{7}\right)=\frac{2}{7}$$ which is a period-3 orbit. Is there any better way of finding a period-3 orbit , more specifically, a period-3 point? I'm currently dual-booting to either Ubuntu 10.10 or Windows XP. However, I rarely use windows and would like to remove it.  I've use the Ubuntu live CD to access GParted. I've also deleted the windows partitions (I think), which were labeled both ntfs and fat32.  I'm just not sure how to extend the Ubuntu partition to cover the unallocated space. Furthermore, how do I deal with the 'key' designations, which state that a partition is busy.  Help! What is the historic present tense? I learned that the historical present may be used to create an effect of immediacy in narratives. I have a question about the historic present tense. Why don't we use the progressive tense instead of the simple present tense?   ※My English skill is poor, so my question might sound rude. But I don't mean to offend anyone. I'd be glad if someone could reply to my question. Find the general solution of $y'= a^{x + y}$ where y is the function Clip tool gives ERROR 000732? notify-osd replaced with dunst after switching back to unity from i3wm I was testing i3wm (sudo apt-get install i3 is what I ran, and chose i3 from the log in screen) on my machine and after a while, decided to switch back to Unity. Upon switching back, I noticed that notifications came in the top right corner similar to i3 even though I was using Unity.  I'd really like it to use the normal Unity notification bubbles instead.  I looked into it and turns out instead of notify-osd, dunst is being used.   I tried using sudo vim /usr/share/dbus-1/services/org.freedesktop.Notifications.service and editing the file, but it has the correct line (i.e. Exec=/usr/lib/x86_64-linux-gnu/notify-osd) as expected.  I also tried unity-tweak-tool --reset-unity but that didn't do anything.  Is it possible for me to return to the normal notifications? Any help would be greatly appreciated. Thanks :)  Edit: I was able to return to the normal notifications by removing i3wm itself (and dunst). What I am actually asking is: is it possible to change to normal notifications while still keeping i3 and dunst on my system?  Note: This is NOT a duplicate of . The solution there is to remove dunst and I would like to keep dunst and have that work when I choose i3, and have notify-osd work when I choose Unity. How do I create tools with multiple properties? 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