modest Posted February 22, 2009 Report Posted February 22, 2009 for [math]n=56[/math], [math]2^{n-1}-13[/MATH] = [math]2^{55}-13[/math] = [math]36028797018963968-13[/MATH] = [math]36028797018963955[/MATH]. While the Numberator chokes on an integer this big, we can see it is divisible by 5 by the last digit. I think you accidentally did [math]2^{n-1}-13[/math] instead of [math]2^{n+1}-13[/math]. I get [math]2^{n+1}-13[/math] = 144115188075855859 and [math]2^n(2^{n+1}-13)[/math] (possible strange anomaly) = 10384593717069654320312270165377024 144115188075855859 is prime, and 10384593717069654320312270165377024 is not divisible by 6. As for being abundant by 12... not sure yet... ~modest Turtle 1 Quote
TheBigDog Posted February 22, 2009 Report Posted February 22, 2009 We are starting to deal with some big numbers now hombres! I understand that I can inherit J# classes into vb.net, which include BigInt; the big as you need it to be number class. I will include that in how the 2K9 version works. As you were then... Bill Turtle 1 Quote
modest Posted February 24, 2009 Report Posted February 24, 2009 Here are the first few factors, T... along with the ongoing sum under each set... 5192296858534827160156135082688512 2 divisor sum = 5192296858534827160156135082688515 2596148429267413580078067541344256 4 divisor sum = 7788445287802240740234202624032775 1298074214633706790039033770672128 8 divisor sum = 9086519502435947530273236394704911 649037107316853395019516885336064 16 divisor sum = 9735556609752800925292753280040991 324518553658426697509758442668032 32 divisor sum = 10060075163411227622802511722709055 162259276829213348754879221334016 64 divisor sum = 10222334440240440971557390944043135 81129638414606674377439610667008 128 divisor sum = 10303464078655047645934830554710271 40564819207303337188719805333504 256 divisor sum = 10344028897862350983123550360044031 20282409603651668594359902666752 512 divisor sum = 10364311307466002651717910262711295 10141204801825834297179951333376 1024 divisor sum = 10374452512267828486015090214045695 5070602400912917148589975666688 2048 divisor sum = 10379523114668741403163680189714431 2535301200456458574294987833344 4096 divisor sum = 10382058415869197861737975177551871 1267650600228229287147493916672 8192 divisor sum = 10383326066469426091025122671476735 633825300114114643573746958336 16384 divisor sum = 10383959891769540205668696418451455 316912650057057321786873479168 32768 divisor sum = 10384276804419597262990483291963391 158456325028528660893436739584 65536 divisor sum = 10384435260744625791651376728768511 79228162514264330446718369792 131072 divisor sum = 10384514488907140055981823447269375 39614081257132165223359184896 262144 divisor sum = 10384554102988397188147046806716415 19807040628566082611679592448 524288 divisor sum = 10384573910029025754229658486833151 9903520314283041305839796224 1048576 divisor sum = 10384583813549340037270964327677951 4951760157141520652919898112 2097152 divisor sum = 10384588765309497178791617249673215 2475880078570760326459949056 4194304 divisor sum = 10384591241189575749551943713816575 1237940039285380163229974528 8388608 divisor sum = 10384592479129615034932106952179711 618970019642690081614987264 16777216 divisor sum = 10384593098099634677622188583944191 309485009821345040807493632 33554432 divisor sum = 10384593407584644498967229424992255 154742504910672520403746816 67108864 divisor sum = 10384593562327149409639749895847935 77371252455336260201873408 134217728 divisor sum = 10384593639698401864976010231939071 38685626227668130100936704 268435456 divisor sum = 10384593678384028092644140601311231 19342813113834065050468352 536870912 divisor sum = 10384593697726841206478206188650495 9671406556917032525234176 1073741824 divisor sum = 10384593707398247763395239787626495 4835703278458516262617088 2147483648 divisor sum = 10384593712233951041853758197727231 The sum already has the factor one in it, although it is not shown in the list. Are we sure that all the factors will be a power of 2? ~modest Quote
modest Posted February 24, 2009 Report Posted February 24, 2009 Are we sure that all the factors will be a power of 2? If that's the case then I get this: 5192296858534827160156135082688512 2 divisor sum = 5192296858534827160156135082688515 2596148429267413580078067541344256 4 divisor sum = 7788445287802240740234202624032775 1298074214633706790039033770672128 8 divisor sum = 9086519502435947530273236394704911 649037107316853395019516885336064 16 divisor sum = 9735556609752800925292753280040991 324518553658426697509758442668032 32 divisor sum = 10060075163411227622802511722709055 162259276829213348754879221334016 64 divisor sum = 10222334440240440971557390944043135 81129638414606674377439610667008 128 divisor sum = 10303464078655047645934830554710271 40564819207303337188719805333504 256 divisor sum = 10344028897862350983123550360044031 20282409603651668594359902666752 512 divisor sum = 10364311307466002651717910262711295 10141204801825834297179951333376 1024 divisor sum = 10374452512267828486015090214045695 5070602400912917148589975666688 2048 divisor sum = 10379523114668741403163680189714431 2535301200456458574294987833344 4096 divisor sum = 10382058415869197861737975177551871 1267650600228229287147493916672 8192 divisor sum = 10383326066469426091025122671476735 633825300114114643573746958336 16384 divisor sum = 10383959891769540205668696418451455 316912650057057321786873479168 32768 divisor sum = 10384276804419597262990483291963391 158456325028528660893436739584 65536 divisor sum = 10384435260744625791651376728768511 79228162514264330446718369792 131072 divisor sum = 10384514488907140055981823447269375 39614081257132165223359184896 262144 divisor sum = 10384554102988397188147046806716415 19807040628566082611679592448 524288 divisor sum = 10384573910029025754229658486833151 9903520314283041305839796224 1048576 divisor sum = 10384583813549340037270964327677951 4951760157141520652919898112 2097152 divisor sum = 10384588765309497178791617249673215 2475880078570760326459949056 4194304 divisor sum = 10384591241189575749551943713816575 1237940039285380163229974528 8388608 divisor sum = 10384592479129615034932106952179711 618970019642690081614987264 16777216 divisor sum = 10384593098099634677622188583944191 309485009821345040807493632 33554432 divisor sum = 10384593407584644498967229424992255 154742504910672520403746816 67108864 divisor sum = 10384593562327149409639749895847935 77371252455336260201873408 134217728 divisor sum = 10384593639698401864976010231939071 38685626227668130100936704 268435456 divisor sum = 10384593678384028092644140601311231 19342813113834065050468352 536870912 divisor sum = 10384593697726841206478206188650495 9671406556917032525234176 1073741824 divisor sum = 10384593707398247763395239787626495 4835703278458516262617088 2147483648 divisor sum = 10384593712233951041853758197727231 2417851639229258131308544 4294967296 divisor sum = 10384593714651802681083020624003071 1208925819614629065654272 8589934592 divisor sum = 10384593715860728500697658279591935 604462909807314532827136 17179869184 divisor sum = 10384593716465191410504989992288255 302231454903657266413568 34359738368 divisor sum = 10384593716767422865408681618440191 151115727451828633206784 68719476736 divisor sum = 10384593716918538592860578971123711 75557863725914316603392 137438953472 divisor sum = 10384593716994096456586630726680575 37778931862957158301696 274877906944 divisor sum = 10384593717031875388449862762889215 18889465931478579150848 549755813888 divisor sum = 10384593717050764854381891097853951 9444732965739289575424 1099511627776 divisor sum = 10384593717060209587348729899057151 4722366482869644787712 2199023255552 divisor sum = 10384593717064931953833798567100415 2361183241434822393856 4398046511104 divisor sum = 10384593717067293137079631436005375 1180591620717411196928 8796093022208 divisor sum = 10384593717068473728709144940224511 590295810358705598464 17592186044416 divisor sum = 10384593717069064024537095831867391 295147905179352799232 35184372088832 divisor sum = 10384593717069359172477459556755455 147573952589676399616 70368744177664 divisor sum = 10384593717069506746500417977332735 73786976294838199808 140737488355328 divisor sum = 10384593717069580533617450303887871 36893488147419099904 281474976710656 divisor sum = 10384593717069617427387072699698431 18446744073709549952 562949953421312 divisor sum = 10384593717069635874694096362669695 144115188075855859 72057594037927936 divisor sum = 10384593717069636090866878476453490 The factors in my previous post were found exhaustively. These were found by checking powers of 2 with the prime at the end. If this is the whole list then the number is unfortunately not abundant by 12. :) ~modest EDIT: You can use this page as a calculator for big numbers:http://gmplib.org/at the bottom under Demo 1 Quote
modest Posted February 24, 2009 Report Posted February 24, 2009 :confused: :doh: :doh: Sorry, C is playing tricks on me. Here are all the factors... 5192296858534827160156135082688512 2 divisor sum = 5192296858534827160156135082688515 2596148429267413580078067541344256 4 divisor sum = 7788445287802240740234202624032775 1298074214633706790039033770672128 8 divisor sum = 9086519502435947530273236394704911 649037107316853395019516885336064 16 divisor sum = 9735556609752800925292753280040991 324518553658426697509758442668032 32 divisor sum = 10060075163411227622802511722709055 162259276829213348754879221334016 64 divisor sum = 10222334440240440971557390944043135 81129638414606674377439610667008 128 divisor sum = 10303464078655047645934830554710271 40564819207303337188719805333504 256 divisor sum = 10344028897862350983123550360044031 20282409603651668594359902666752 512 divisor sum = 10364311307466002651717910262711295 10141204801825834297179951333376 1024 divisor sum = 10374452512267828486015090214045695 5070602400912917148589975666688 2048 divisor sum = 10379523114668741403163680189714431 2535301200456458574294987833344 4096 divisor sum = 10382058415869197861737975177551871 1267650600228229287147493916672 8192 divisor sum = 10383326066469426091025122671476735 633825300114114643573746958336 16384 divisor sum = 10383959891769540205668696418451455 316912650057057321786873479168 32768 divisor sum = 10384276804419597262990483291963391 158456325028528660893436739584 65536 divisor sum = 10384435260744625791651376728768511 79228162514264330446718369792 131072 divisor sum = 10384514488907140055981823447269375 39614081257132165223359184896 262144 divisor sum = 10384554102988397188147046806716415 19807040628566082611679592448 524288 divisor sum = 10384573910029025754229658486833151 9903520314283041305839796224 1048576 divisor sum = 10384583813549340037270964327677951 4951760157141520652919898112 2097152 divisor sum = 10384588765309497178791617249673215 2475880078570760326459949056 4194304 divisor sum = 10384591241189575749551943713816575 1237940039285380163229974528 8388608 divisor sum = 10384592479129615034932106952179711 618970019642690081614987264 16777216 divisor sum = 10384593098099634677622188583944191 309485009821345040807493632 33554432 divisor sum = 10384593407584644498967229424992255 154742504910672520403746816 67108864 divisor sum = 10384593562327149409639749895847935 77371252455336260201873408 134217728 divisor sum = 10384593639698401864976010231939071 38685626227668130100936704 268435456 divisor sum = 10384593678384028092644140601311231 19342813113834065050468352 536870912 divisor sum = 10384593697726841206478206188650495 9671406556917032525234176 1073741824 divisor sum = 10384593707398247763395239787626495 4835703278458516262617088 2147483648 divisor sum = 10384593712233951041853758197727231 2417851639229258131308544 4294967296 divisor sum = 10384593714651802681083020624003071 1208925819614629065654272 8589934592 divisor sum = 10384593715860728500697658279591935 604462909807314532827136 17179869184 divisor sum = 10384593716465191410504989992288255 302231454903657266413568 34359738368 divisor sum = 10384593716767422865408681618440191 151115727451828633206784 68719476736 divisor sum = 10384593716918538592860578971123711 75557863725914316603392 137438953472 divisor sum = 10384593716994096456586630726680575 37778931862957158301696 274877906944 divisor sum = 10384593717031875388449862762889215 18889465931478579150848 549755813888 divisor sum = 10384593717050764854381891097853951 9444732965739289575424 1099511627776 divisor sum = 10384593717060209587348729899057151 4722366482869644787712 2199023255552 divisor sum = 10384593717064931953833798567100415 2361183241434822393856 4398046511104 divisor sum = 10384593717067293137079631436005375 1180591620717411196928 8796093022208 divisor sum = 10384593717068473728709144940224511 590295810358705598464 17592186044416 divisor sum = 10384593717069064024537095831867391 295147905179352799232 35184372088832 divisor sum = 10384593717069359172477459556755455 147573952589676399616 70368744177664 divisor sum = 10384593717069506746500417977332735 73786976294838199808 140737488355328 divisor sum = 10384593717069580533617450303887871 36893488147419099904 281474976710656 divisor sum = 10384593717069617427387072699698431 18446744073709549952 562949953421312 divisor sum = 10384593717069635874694096362669695 9223372036854774976 1125899906842624 divisor sum = 10384593717069645099192033124287295 4611686018427387488 2251799813685248 divisor sum = 10384593717069649713129851365360031 2305843009213693744 4503599627370496 divisor sum = 10384593717069652023476460206424271 1152921504606846872 9007199254740992 divisor sum = 10384593717069653185405164068012135 576460752303423436 18014398509481984 divisor sum = 10384593717069653779880314880917555 288230376151711718 36028797018963968 divisor sum = 10384593717069654104139488051593241 144115188075855859 72057594037927936 divisor sum = 10384593717069654320312270165377036 It is abundant by 12, it is a strange anomaly :) ~modest Quote
modest Posted February 25, 2009 Report Posted February 25, 2009 So Modest, do you understand what Bombdy did to get this? I'm still befuddled. :eek2: Well... I'm not entirely sure. It looks like—if you write the factors of 304 as an example:Noticing 19 is prime and 16 is a power of 2, this can be generalized such that,The factors on the left can be summed,[math]\sum_{i=0}^{n}2^i[/math]and on the right (with the exception of 304 since you don't add the number itself as a factor,[math]\sum_{i=1}^{n} 2^{n-i} \cdot p[/math]When these numbers are summed they will need to be 12 greater than the number being factored. The number being factored can be written as 16 x 19 or [math]2^n \cdot p[/math], so this gives an equality,[math]2^n \cdot p + 12=\sum_{i=0}^{n}2^i+\sum_{i=1}^{n}2^{n-i} \cdot p[/math]Bombadil then rewrites the right hand side as,[math]2^{n+1}-1+(2^{n}-1)p[/math]making the equality,[math]2^n \cdot p + 12 = 2^{n+1} -1 + (2^{n}-1) p[/math]and rearranging,[math]p=2^{n+1} - 13[/math]It's quite ingenious if you ask me. Before we get too drunk with euphoria, let's remember that this expression/equation Bomby gave us does not give us the Strange Anomaly 54 and so we can't assume there aren't other anomalies of that form.Right. The factors of 54 don't follow the power of 2 format, yet it's still abundant by 12 and still can't be divided by 6. So, we can say any solution to Bombadil's method should give a strange anomaly, but others do exist. ~modest Quote
modest Posted February 25, 2009 Report Posted February 25, 2009 Back on the ground, I waited all night before posting to correct Modestino's last bit above, as I thought he'd be back & put in the fix. Do y'all see it? :confused: Well, obviously 54 does divide by 6, as 6*9=54. 54 is a Strange Anomaly though, as 9 is not Prime. 6 and non-prime I can't seem to keep my strangeness straight ~modest Quote
Bombadil Posted March 1, 2009 Report Posted March 1, 2009 Bombadilo, I would love to hear you talk about what exactly you saw that put you on this and other gory details from this result of the mathematical & insightful kind. I was just looking at your list of strange numbers wondering if it would be possible to generate more of them when I noticed that on all but one of them one of the numbers have a number of the form [math]2^n[/math] as one of the factors. After considering a few things that wouldn’t work I realized that the number could be factored out as [math]2^np[/math] where p was a prime number. Writing it like this makes it relatively easy to add up the sum of the factors as well as making the question of what value to give the prime a seemingly obvious question. As for what to do next, I haven’t tried writing it out yet but I suspect that by choosing the form of a strange number as [math]2^npq[/math] with p and q being primes such that [math]p\neq q[/math] and [math]p,q>3[/math] and solving for one of them, that a contradiction may be reached but I haven’t had the chance to try it to find out for sure so maybe its just a dead end. P.S. I see that it also can easily be used to generate strange numbers in other number sets as well so I wonder what other patterns might be found with it. Quote
Rade Posted June 29, 2010 Report Posted June 29, 2010 Most likely this is off topic, but here is an observation about this comment: Take a pile of twelve beans. How many ways can you divide then into equal piles? One pile of twelve, two piles of six, three piles of four, four piles of three, & twelve piles of one.QED :shrug:What about, 6 piles of 2 ? Do you not need the opposite of 2 piles of 6 ? So, for number 12, you have a "strange number rule" of "opposites piles": 1 pile 12 and 12 piles 12 -- 6 and 6 -- 2 (add word pile(s) as needed) 3 -- 4 and 4 -- 3 (note: 5, 7, 9 never enter the rule) == OK, let us look at 12 * 2 = 24 1 -- 24 and 24 -- 12 -- 12 and 12 -- 23 -- 8 and 8 -- 3 4 -- 6 and 6 -- 4 (again 5,7,9 never enter the rule) == (this is fun) 24 * 2 = 48 1-- 48 and 48 -- 12 -- 24 and 24 -- 2 3 -- 16 and 16 -- 34 -- 12 and 12 -- 4 6 -- 8 and 8 -- 6 (again no 5, 7, 9 ), but I do see that you add 1 "opposite pile" each time you multiply by 2 ) 48 * 2 = 96 1 -- 96 and 96 -- 12 -- 48 and 48 -- 2 3 -- 32 and 32 -- 34 -- 24 and 24 -- 46 -- 16 and 16 -- 6 8 -- 12 and 12 -- 8 (5, 7, 9 are no fun at all)== Let us look at 5, 7, 9 to see what is going on: 12 / 5 = 2.4000000000000000000.....(infinity, a repeating decimal 0)24 / 5 = 4.8000000000000000000....48 / 5 = 9.6000000000000000000....96 / 5 = 19.200000000000000000.... (well, 5 likes infinity) --12 / 7 = 1.71428524 / 7 = 3.428571448 / 7 = 6.857142896 / 7 = 13.714285 (I see a repeating pattern for 7) -- 12 / 9 = 1.33333333333333333333333....(to infinity)24 / 9 = 2.66666666666666666666666.....48 / 9 = 5.33333333333333333333333.....96 / 9 = 10.6666666666666666666666.... (wow, a "repeating" repeating decimal for #9--first .33..then .66..then ..33..then..66) Maybe 5, 7 9 are fun after all == OK, that was fun but I have absolutely no idea what it means, except I did not have to cut the grass. Quote
Gordon Freeman Posted August 2, 2010 Report Posted August 2, 2010 I ask the same question, why is twelve so special? I had heard about five being used within a special calculus formula in which sequences can be cracked like MD5 hash generators, but twelve makes no sense. And even if it is important, what can these numbers be used for? If it's just to simply make a mathematical code, then it can just as easily be cracked. In fact, the only mathematical coding that has proven to be uncrackable thus far is nonfigurative sets. Special numbers can be easily solved for, so again, what is their significance? Quote
Gordon Freeman Posted August 4, 2010 Report Posted August 4, 2010 My only resources are my colleagues and my notebook that I've written some sequences into. I have a friend that uses this site that could help you much more greatly than I; his user-name is IDMclean. He knows quite a bit more about non-figuratives than I do. If you need anything on physics, gravito force theory, therma-fluids, or time thread theory, I'd be glad to talk some more. Turtle 1 Quote
Rade Posted August 24, 2010 Report Posted August 24, 2010 hello turtle, Not sure if you have noticed this, but there is a "perfect" (r^2 = 1) linear relationship when you log transform both sets of numbers (x,y plot) in the sequence below. You will see that all of your "numbers" (12-strange, 56-bizarre, 992-peculiar, 16256-curious) are included in the set of y numbers, plus a few others. x y4 -- 128 -- 5616 - 24032 - 99264 - 4032128 - 16256 Quote
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