Fourier Help required on Giant numbers

[mikeburr]

dear all
im not sure the post shd go here but i expect we might get some interesting programs resulting so on that basis .. heres my Help request ...

im looking for a FOURIER FRIEND .. as i don't do Fourier [ i fancy its a bit like Floating Point Coke !!!]

i thought this might amuse you as it did me


here is the result of an analysis i ran on the number 7
it produced the numbers  7 22 37 46 51 53 54

here is 54 / 7**2 [54/49]

1.10204081632653061224489795918367346938775510204081632653061224489795918367346938775510204...
: 102040816326530612244897959183673469387755 : .........................

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;   getting side tracked ;  notice power of 2 build_up
.10204081632653061224489795918367346938775510204081....   
  1
    2
      4
        8
         16
           32
             64
              128
                256
                  512
                   1024
                     2048
                       4096
1.1020408163265306122448     

why powers of 2  per 100 :   49 = 100/2 - 1    prob
;;;;;;;;;;;;;;;;;;;;;;;;;;  end of side track ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;   

: 102040816326530612244897959183673469387755 : .........................
you will prob have also noticed that the division repeats itself every 42 [7*6] digits in this case starting

this is because there is no other common factor in 54 [ 2 3 3 3 ] and 49 [ 7 7 ] and 1/7 has a sequence 6 digits long 142857 repeated

142857 has a subsequence .. which is reflexive around its mid point ie digits {1 :4 } 1+8 = 9  similarly{2,5}  4 + 5 = 9 and lastly{3,6}  7 + 2 = 9
.. a similar six digit repeating pattern can also be made by dividing 1 by 13 .. a seven digit one by dividing 1/239 or 1/4649


Now what im interested in is to see if theres any sub_patterning that im missing by my Old Cut up Back [ Of Threatening and Abusive ] Letters
Approach to this and i dont know enough about Fourier or feel confident enough to know how to approach this sort of Digital Signal Processing
and the matrix manipulation etc involved [ does Fast Fourier cheat and use powers of 2 ??? somehow]




[if possible i would like somebody to preferably send me the code to compile to make a Fourier machine and help with a load of hand holding advice
or write it for me to a specification .. or ... at least run the examples through here .. i  calculated them to 4000 digits but it looks weird putting 4000 digit numbers up [ bad enough with the longer ones at the end ...but there should be no prob with Fourier windowing ???
except at ends .. but they shd prob be extended to a couple of multiples of the sequences  ]

here are a few other divide by 49ers and then some natural numbers whose period is length 42  and lastly some division by primes 

53   53/7**2 =      1.0816326530612244897959183673469387755102040816326530612244897959183673469387755102040816326530612244897959183673469387755102040816326
51   51/7**2 =      1.04081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632653061224489795918367346938775510204081632
51   51/127  =       .4015748031496062992125984251968503937007874015748031496062992125984251968503937007874015748031496062992125984251968503937007874015748031496
53   53/127  =       .4173228346456692913385826771653543307086614173228346456692913385826771653543307086614173228346456692913385826771653543307086614173228346456
61 related [60 sequence]  1/7061709990156159479 =
                     .00000000000000000014160876068175754265293767145130197783818810000000000000000001416087606817575426529376714513019778381881000000000000000000141608760681757542652937671451301977838188100000000000000000014160876068175754265293767145130197783818810000000000000000001416087606817575426529376714513019778381881000000000000000000


508 related 1/651871849785243820958119684233142982170536938147349501049955875423544371888519632103159753836519854149224951224466197

      .0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000015340438467000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001534043846700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000153404384670000

508 related 1/36099531273603138218699301565567581705151216702113889

      .0000000000000000000000000000000000000000000000000000277011907002577759809351546432595468773761912508656994814208603377753775008999999999999999999999999999999999999999999999999999972298809299742224019064845356740453122623808749134300518579139662224622499100000000000000000000000000000000000000000000000000002770119070025777598093515464325954687737619125086569948142086033777537750089999999999999999999999999999999999999999999999999999722988092997422240190648453567404531226238087491343005185791396622246224991

557 related 1/ 652065570931334169846518762110895357104035953330623783530923329412897765703841859492780362601926814638167836591846272150911969126521

      .0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000015335880999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999998466411900000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000153358809999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999984664119

557 related 1/ 9327281575040435942820030416618073853906181206383845973140973454310325710523151012873614569275960380714495413018734336834397

      .000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000107212373932826700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010721237393282670000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001072123739328267

646 related 1/ 87946415928437692466120948982620559202657683736102165146501778626343706150135447983693977813544625674393856438133847360929077123212993     

     

.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001137056001024195815194290511343443143005491829797403110282872499864240721542199028198482013788729478306493143786348560286831829515442126300920690295896223002530727965266138037375581216950509954291219984328950313346778356708942819787839911117533016927759459302447351433651815763360801313594983368126355886555438297901738130801412298450517327488747635043231498919414396599756029980135274533364216951817843322816605095839339074151818309632342884552257877434578453443366296912212291805009422383125230282720768344941430000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000113705600102419581519429051134344314300549182979740311028287249986424072154219902819848201378872947830649314378634856028683182951544212630092069029589622300253072796526613803737558121695050995429121998432895031334677835670894281978783991111753301692775945930244735143365181576336080131359498336812635588655543829790173813080141229845051732748874763504323149891941439659975602998013527453336421695181784332281660509583933907415181830963234288455225787743457845344336629691221229180500942238312523028272076834494143


im interested in 508 because it looks like 509 1's [ie 111111111.. 509 times ] doesnt seem to factorise and i have a reason that links this to
the fact that 647 doesnt and the same idea links 19 and 23 but ive ABSOLUTELY no idea why !!
and thought fourier might help by looking at it
i also think that 557 1's may factorise but have yet to finish the program to test it and wondered if Fourier might show something  [ any observations thankfully received
as you may have the answers i dont !! .. usually the way  ]   

regards   mike b   

[K_F]

Read this - You won't be sorry ;)

http://www.dspguide.com/swsmith.htm

[mikeburr]

thanks KF
funny enough ive read a few of his [Dr Smiths] many posts on the web relating to electronics and the origins and nature of noise in systems but not his book as yet so ill try that .. the thing is im only really after knowing if the [Im] part of the Fourier is offering anything ... the [Re] part will prob reveal the factors that are part of the number stream .. i didnt disclose these factorisations in the original as i didnt want to pre_prejudice anyone kind enough to run the number stream through Fourier .. there are indeed a few pages of which Free small FFT in multiple languages by  LiaoMI are excellent and well presented starting points .. but ive no real handle on the subtleties of doing Fourier as havent the years of hard won experience that some of the members here have ....so its a long learning curve for what i suspect is prob Not Much Gain
Aside and some thing id like to try on the sequences
Many years ago i wrote a Fourrier to analyse the banding that was occuring [due to oscilllation] of a rotating drum .. this was very basic and only took in the first 7 harmonics ... i then made a subsequent version that worked entirely differently by using predefined shapes eg ramp functions [Read : not neccessarily orthogonal ] and removing them from the source until i was left with the Statistical problem of determining Noise hence the Ref to Dr Smith above ... the few mathematicians that i know scoffed at this idea !! but it was very effective  .. i shd add perhaps obscurely that symmetry is not a proof in some mathematics
regards   mike b