Strange Numbers

[TheBigDog]

Turtle, the Numberator is running. When you get settled in after your move give me a heads up and we will see how we proceed. I will let it run until then. I wonder how high it will search?

 

Bill

[TheBigDog]

List so far...

 

304
4544
9272
14552
25472
74992
127744
170612
353672
396112
458144
495104
857312
1006496
1243808
1764512
4041152
4860050
5888672
6019264
9865304
11627864
12445504
13170104
15317696
17135864
20220344
33058112
33501184
34699904
35019968
38943104
41162624
44818304
50908472
53032832

Searched through and past 84000000 and going. Progressing at around 1300/second. But need to move to a dedicated machine.

 

Bill

[TheBigDog]

I have about a day and of half of service yet, & I have kept checking your progress in between packing & cleaning. I read (& copied:lol: ) the list last night & woke early today with it on my mind. At first glance they all seemed to divide by 4, but then there was that pesky 4860050, which does not have 4 as a factor, but does have 5; strange indeed!;) :lol:

On the idea of divisors of these anomolous Strange numbers, it may prove helpful to also save to file the list of divisors with each of them and so by extension how many divisors.

Have you seen anything to catch your special attention? This is all very exciting to me & I very much appreciate your interest & especially your programming work. By all means post any questions or observations; I'll return as soon as possible. (That goes for others as well.)

Thanks ever so much Bill!B)

Turtle

Turtle,

 

This list was a bit of a tease. I have every aspect of these numbers. The search is at 308,000,000 right now. It is getting progressivly slower as the numbers get bigget. I have stopped it a couple of times to tweak the search process and get more speed. It is analyzing just over 1700/second at this point. Not the most powerful computer in the world, but doing its damndest. Time is the great equalizer.

 

It has found 44 exceptions now. To me the most interesting are the one divisible by five that you mentioned above, and 126083072. Peculiar, 14 pairs including 2^13 When you get back online I will send you all the data and all the toys. B)

 

Bill

[TheBigDog]

Sweet po Pete! The main part of my move is complete & the cable guys came this morning to get me back on the web. I will have my notes on the topic unpacked soon.

In the vein of the origins of this research, I may have said earlier in the thread that I started the computer search using an 8088 clocked at 8 Mghz & 1700 per sec is simply amazing to me. Do you have the fields displaying real time? Do you have Katabatak transforms of the sets? Different bases?:hihi: :lol:

I gave some thought to just how big a number really makes sense to look at, that is a number running more than a single line is difficult to view for patterns.

That's all that pops to mind just now, except to say woot woot & what'a ya know bout dat!:phones:

Welcome back my hard shelled hombre!

 

Here is the Numberator as it exists today, along with the files that make it tick. When all the peices are detached to the same place and you run it you can analyze all the numbers and have it continue the search. I have a function for Katabataking a number, but only in base 10 so it is not visible yet. I am trying to add flexible basing to the set to make it more diverse, but I have not figured out how to build that into the program yet.

 

On my laptop it runs at just over 1400 per second now, and is almost to half a billion. I am making a comfortable home for it to just run unmolested. Slower computer, but if we are patient it will get through many many computations. I had been keeping the hole set of strage numbers, but the file got enormous, so I started to just keep the expections. I can go back and get the full set later.

 

Bill

[Boerseun]

The strangest number I've come across so far is eleventy-seven.

[Racoon]

I'd love to be more help fella's!

But I'd probably get in the way more than I'd help...:lol:

 

I'm smelling the burning brain cells all the way over here!

I will stay alert to your findings...

 

How high a number do you Gents plan on reaching?

Is this something that can go on forever? Past one hundred Million Trillion Gazillion?? ;) :hihi:

 

Strange indeed, and Loving it! :phones:

Rascally Rapscallion

[Racoon]

I couldn't download BigDogs zip file. ;) :hyper:

said it was "corrupted"

 

The more mistakes, the more you learn! :hihi:

Racoon

[TheBigDog]

Whoa! Point of order. I dug out my notes & in going over my list of anamolous Curious Numbers I have some not in the Numberator's list:

I have the first Anomalous Curious as 48684 with 6 pairs of divisors & 112952 with 8 pairs of divisors.

Is this my error somehow?:eek: Yours BigDog?:) The Numberator's? ;) Bryan's?:)

Another point: While refereing to the 'flukes' we have gone looking for as "anomolous" I misspelled it "anomolous" quite a lot, and on the ohter hand Big, you refer to them as "exceptions" & misspelled it as "expections". I propose we correctly spell and call the target(s) of our hunt(s) "Exceptional" Strange, Bizarre, Curious, etc. Numbers.

Finally, I find I have a set name after Quirky, which is "Freakish": I think the first is 25769607168.

Finally finally, I await your response. (unless of course some new stray thought bounds into my caranium:hyper: )

Turtle Out

Issues noted. Added to the "to do" list.

 

I am making the category names user configurable. I am checking the math on the numbers you have indicated. I am finding the dictionary. And the other things I have mentioned are being done too. #3 is taking the fall if I can't figure these out. :eek:

 

These truely are the best of times!

 

Bill

[TheBigDog]

Whoa! Point of order. I dug out my notes & in going over my list of anamolous Curious Numbers I have some not in the Numberator's list:

I have the first Anomalous Curious as 48684 with 6 pairs of divisors & 112952 with 8 pairs of divisors.

Is this my error somehow?:eek: Yours BigDog?:eek2: The Numberator's? :eek_big: Bryan's?:eek2:

I check these numbers. The second is indeed Curious, but has perfect number 28 as a factor, so it is not anomalous, or Exceptional. The first is also curious, but has perfect number 6 as a factor. I am adding a tool to the Numberator for entering and testing any number of your choice to aid in this type of research!

 

Bill

[TheBigDog]

Whoa! Again.:eek2: This is a new discovery & merits closer scrutiny. Remebering that the standard run-o'-the-mill Curious Number has 14 pairs of divisors, so my two 'exceptions' differ in this regard. I feel confident to say it's an instance of 'Exceptional Anomalous Curious Numbers'.

Moreover, the run-o'-the'mill Curious Number is abundant by twice the Perfect 8128, not 6 or 28. This is more-or-less the set definition as I laid it out.

Speculatous interuptous; someone came in to talk to me & I lost my train ....

Hmmm.... Just a bump in the road. That is why I keep my knees bent while doing math at high speed.

 

Here is the process that the program is doing.

 

1. See if the number qualifies for the "strange" family by comparing the sum of factors to the number
   
2. If the number is perfect add to the list of perfects and move to the next number
   
3. If not in the strang family throw it away and move to next number
   
4. If in the "strange" family check to see if any of the factors are perfect
   
5. If any of the factors are perfect then list as a normal strange number
   
6. If none of the factors are perfect then list as an anomalous strange number
   

 

I take it from your notes that I may have an error. Should I only be checking numbers against their own root perfect number, so to speak?

 

Bill

[TheBigDog]

Just looking over my lists & I spotted 9424. It is the ninth Peculiar Number & it has the first exceptional Strange Number paired with a prime as factors (304*31)

I seem to have misplaced my list of exceptional Peculiars.:eek2:

I am going to put the factors into a list that shows info about each one. What are some of the qualities of the factors that you want at your fingertips?

 

Bill

[TheBigDog]

Yes, that sounds like the solution. I set my test for Strange for example by looking for abundance by 12. Early on when I first found the sets I did not even realize the 'abundance amounts' were double the Perfect Numbers. That's serendipity.:eek_big:

The main exception(s) then have no 'root Perfect' factors & a different number of factor pairs than standard issue.:eek2:

That may make it even faster!

 

Bill

[TheBigDog]

OK, I have my work before me. I will give an update soon. This will be Numberator 2.0 - Rise of the Katabatak! (with definable base)

 

Public Function k(ByVal num as Long, Optional ByVal base as Integer = 10)

 

Bill

[TheBigDog]

Progess progresses. I bit off a bigger peice than I had estimated, but it is tasty to chew on. More later.

 

Bill

[mocnarf]

Even though I am not a mathematician, I have found this discussion quite interesting. I hadn't heard of "Perfect" "Strange" and various other types of numbers. But the discussion got me thinking about ways to find other sets of numbers that would be very unique. For instance:

 

1) Find a set of perfect numbers that the factors of which

add up to a value that is exactly 1 number greater

or 1 number less than a prime number

 

(I would think this would be a considerably more rare occurance.)

 

or how about

 

2) Find a set of numbers that when (integer division) divided by the number of it's factors equals a Prime number but x can not be a prime. x n = p by integer division I mean remainder is discarded and only the whole number is considered .

Examples of x would be:

8, 10, 18, 21, 22, 24, 28, 33, 35, 39, 40

 

where n = number of factors in x and wher the result p is a prime

 

I wonder if a set such numbers would ever have a special name? How about "Francomian" :phones:

[bpjg2fat]

hah, wouldn't it be funny if it was just a random number generator

[bpjg2fat]

id laugh. :xx: