h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

hello not run into you before

what you up to????

Oh, I've been dabbling with the 3n+1 problem; writing lots of software and scribbling and bibbling. I don't think anybody ever looks at this stuff unless they're somehow compelled. It's nice to get some kind of reply though.

have you run into julzes yet, though hes now calling himself xiory or something

he is driving everyone nuts with some sort of numerology, god alien theory of his

would be nice if a math wizz had a look at his stuff??

Julzes appears to be laying low; I could find only one reference to him. I must be an old fuddy-duddy; this Internet jargon is almost incomprehensible to me. It's pretty bad when an American is a guardian of the Queen's English.

this is his PS

http://www.bbc.co.uk/dna/h2g2/brunel/U14075709

maybe you could make head or tail of his math??

I know this conversation exists despite Taff's rapidly removing it from his space, and since it was motivated by me I thought it appropriate to join in.

First of all, hello from me as well. We haven't met and I see you are good with mathematics, which I am also, but also good with programming. So, I will start with what I'm working on where you might assist or, actually, take charge. It is largely but not entirely seperate from what Taff calls numerology (and I can't argue). Here is the relevant link to the Online Encyclopedia of Integer Sequences: http://www.research.att.com/~njas/sequences/A152396

I'm currently looking for any seven-digit fourth term there might be in this sequence, having pretty much ruled out (a lot of scanning, so subject to human error) everything up to 5 million right now. It's quite unusual for Mr. Sloane to accept a sequence that doesn't already have four known terms, so be sure to look at it, its companion (A152397), and the really surprising sequence (work on simultaneous solutions of 'x^2n+x^n-1=prime for many small n' by a fellow known as PrimeHunter at wikipedia's mathematics help desk shows x=10 is very unusual in relationship to it) I rediscovered that gave me the idea to look for something else (A096594). When I finish seven-digit numbers the way I'm doing it, I would like to be done one way or the other, either having found the next term or knowing someone will shortly by computer (and even if I find what I believe is the solution, a good check with a program will be best). The way I am operating is with by-eye searches of the largest of the four candidates from batch-primality-testing lists, followed by comparison to another list for the next-to-largest, followed by, if necessary, checking the smallest then next-to-smallest in turn. I've probably reached stage four (the next-to-smallest) about 10-15 times, so you can imagine I feel close to getting a result.

If you're interested, I'll let you know where you can get a primality-testing module you can make into a subroutine in some way if I find something, but probably the best thing to do (if you're interested and don't already have such) is to find the long discussion I was having with PrimeHunter on his talk page, introduce yourself there, and ask him the specifics that you need for this task. He's moved on to some record-size prime research with his computer time, but I think he can answer the specific questions you might have about the task at hand.

If you'd like my opinion on your Entries, I will read them all. Just let me know if my opinion is what you're interested in. As far as my really weird mathematics coincidences are concerned--and these involve dates in the common calendar in some cases--I would be happy to have you join in the debate over any subset of what I have been trying to argue. My preferred media for this are the Peer Review threads of the two entries I tried to get through when I first came to hootoo and a couple of the discussion threads, one of which I created and the other of which I seem to have taken over to some degree. I'll point you in the right direction.

I apologize in advance if either of you feel I have barged into a private conversation.

JGM

My mistake. The conversation drops quickly below radar because of the large number of conversations Taff holds. A little paranoia, I guess you could say. It was found in a rare moment.

i seem to have dropped him on you

Taff: Why didn't you do as I suggested and tell him my recent maths interest has been in something often called Smarandache sequences?

because i wanted them to make up their own mind!!!!! so i didnt give them details.

thanks for butting in

Thanks for handling things so well yourself. Apologizing for dropping me on him is not exactly in line with what you've just claimed. I was quite reasonable in my posting, and you could have said something else. Now, I'm not saying another word here unless addressed by smallfrey. You can message me if this must continue.

see!!!!

that the sort of guy he is

One of my guide entries is on a generalization of one of the Smarandache functions. It involves the intersection of equilateral triangles in Pascal's triangle. I've only scratched the surface of this topic, but I think it is quite interesting. You're welcome to take the baton and run with it.

In the meantime, I'll take a look at what you're doing. I do have some C programs for primality testing, but they're specifically geared for factoring numbers of the form (a**n+b**n)/(a+b). I've written C programs for doing multiple-word arithmetic (addition, subtraction, multiplication, and division). (If you're interested, I'll send them to you. They've been thoroughly tested.) For really computationally intensive work, I use a TMS32064 signal-processing board with hand-optimized assembly language (at one time, I had about half a dozen of these boards working on one problem). You can purchase one of the boards (USB compatible) for about $500 and get set up to do some serious number crunching. I see that there are computer languages specifically designed for multiple-word arithmetic ("Mensanator" uses one for his 3n+1 work and handles some really huge numbers), but I don't have access to any of them.

and in english????

My present situation regarding the kind of material you've offered to send is that I only have to figure out how to incorporate a full big number package (doing a bit more than you suggest yours does) into my programs. It should be relatively easy, but I won't be getting around to it for a while. I may look into the TMS32064 at some point, though.

I take it that Mensanator is another hootoo person I had not heard of. Are you attempting statistical analyses of the 3n+1 problem or "simply" crunching a lot of numbers in the hopes of perhaps finding a counterexample to what is assumed? I put "simply" in quotes because I did take a brief look at what you've done with the subject, and it's not that simple. Not at all, though I'm sure a careful look will make it clear to me what you have been up to there.

I'll look first at the one Entry you say I might run with when I get done with this 10 million (or before if I find a solution), though I am not sure whether you are looking to have it made Guide-ready or if you are simply indicating I should get into it personally for my own edification, and then I'll also look at the others. The 'Smarandache' thing is just an odd coincidence--unrelated subject matter.

Details of my mathematical competence you may want to know: A large number of graduate courses in mathematics, one course in C, status as an ASA (lapsed) and very rusty at just about all of it. I've been goofing off and studying physics more than pure math when I've been studying at all. I was a top-notch contest person in high school, but then got sick. I've spent most of my time worrying about how to get myself married and how to quit smoking cigarettes. Probably more info than you want, but perhaps it gives something of a picture.

I found Mensanator by googling, so I know I presumed wrong.

I think I will take that offer of the C programs, just because reading them should prove helpful in improving my skills. You will of course have found that my e-mail address is listed with my OEIS entries. Thanks in advance.

Sorry for all the jargon; it's specific to people who do number crunching.

no worries

i do the same with other millitary types, you start talking in acronyms, abreviation and slang and everyone thinks we talk a different language

There are plenty of other people trying to find loops in the 3n+1 sequence or trying to find an initial n value that results in an unbounded sequence. Eric Roosendaal has a good website on this. When I first came to h2g2, I tried to get an article on the 3n+1 problem accepted as an Edited Guide Entry. In retrospect, I see that I was barking up the wrong tree. If I wanted to do serious mathematics, I should have gone to a math house like PlanetMath. I haven't been able to strike a balance between making articles devoid of content and making them appeal to the layman. The recent article on the Four Color Map Theorem is a good article for h2g2 and in my opinion is a good template for mathematically oriented h2g2 articles.

If you have the interest, you can research the generalized Smarandache function that I came up with. It might be suitable for an Edited Guide Entry. Most people have heard of Pascal's triangle and pictures of the equilateral triangles within Pascal's triangle could be shown. I've got too many other interests to pursue this.

I'm not up to speed on factorization. I do know that there are sophisticated techniques for doing factorization. There is a website on Mersenne numbers that mentions doing factorization using the Fourier transform of all things. Mollin's book on algebraic number theory has a section on factorization.

P.S. I'm just an empiricist and am not a mathematician of any merit. I'll get my C programs together and send them to you.