Recent content by jleach

After going on a ghost tour over Halloween, several people were able to take photos of ghosts seen through an old hotel window, a few stories above our position. This got me to wonder if this was a trick that relied on the way that the digital cameras may be able to detect non-visible...

I have seen this or a similar explanation in number theory or combinatorial texts that touch upon number theory, but I don't find it to be a satisfactory solution. The reason is because the solution is actually a problem. Sort of like counting the number of dogs by counting their legs and...

The first thing that you'll have to do when to step out of college is stop thinking like an academic. I've been there, and I was a fool. The classes you take and the degree you earn are similar to merit badges for a boyscout. The real world wants to you earn your merit badge everyday. Only...

It is well known that your genome can respond to the environment, but these responses are not believed to result in an inheritable trait. If you exercise, you can become a body builder, but this won't make your children any stronger. Environmental stress can trigger the activation or...

I consider myself to be a mathematician, but I ended up getting my undergraduate degree in Biology, a master's in information systems, and I'm currently working as a chemist. I promote college, because it's good to have more options available to you, and I believe that math or science degrees...

DNA and protein structures are described at different levels, because the 3-D structure significantly impacts the activity or message. The sequence is merely the primary structure and is usually considered to be the most telling bit of information. However, gene regulation and translation can...

Nothing comes to me yet. I'll just put it in my back pocket and maybe I'll find a use for it someday. Sorry, I was more interested in just sharing my observation than looking at how it could be applied, so I didn't catch that it didn't save any work in finding factors. Finding the factors...

But, that would be changing the rules. Negative numbers aren't allowed. I've done a lot of work studying integer partitions, and I've even started looking at a more complex case by making it N distinct objects instead of N parts. This changes the rule slightly. I'm still not interested in...

Thanks for making me take another look, because I can already see something else that is interesting. If I look at the spacing between actual factors found by my method, there seems to be a symmetry. If this is real, then it could be useful.

You have a point. I think that it's still an interesting observation, but let me think on it and I may be able to find a modification that will improve the method.

When looking for potential factors of an integer, I noticed that I could predict the frequency of the greatest integer function quotient and use this prediction to jump to the next potential factor. See the attachment for an example. I don't know if someone else had already discovered this...

Integer partitioning can not be described algebraically and is often confused for being a combinatorial problem. The fact is that it is a fractal pattern. See the attached table for a breakdown on the frequency of ways that an integer can be divided up into a given number of parts. The stage...

FYI, You can generate a new table for partitions without repeats and it is also a fractal, but with a slightly different rule. I thought that I'd mention this, because if you are only interested in partition sequences without repeated values, then this approach may be a faster computing method.

P.S. If by chance you get a table coordinate with negative numbers, the table value is zero. Example: Column 4 Row -3 = 0

I'm back and I've reviewed my notes. Restricted partitions is a little more complex than I described above, but not bad. The first thing that you'll need is a partition table like the one that I posted on Wikipedia (Search for "Integer Partitions" or "Partition (Number Theory)", then look...