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fourier projection of the primes -> [Fwd: SEQ FROM Roger L. Bagula]

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  • Roger Bagula
    Chaotic sequences made up from a Fourier projection of the primes normalized to the number of Fouriers bases used in the sum. The functions are infinite , but
    Message 1 of 1 , Sep 13, 2003
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      Chaotic sequences made up from a Fourier projection of the primes
      normalized to the number of Fouriers bases used in the sum.
      The functions are infinite ,
      but difficult to calculate with an infinite / full Fourier basis sum.
      -------- Original Message --------
      Subject: SEQ FROM Roger L. Bagula
      Date: Sat, 13 Sep 2003 13:07:27 -0400 (EDT)
      From: <njas@...>
      Reply-To: tftn@...
      To: njas@...
      CC: tftn@...



      The following is a copy of the email message that was sent to njas
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      Subject: NEW SEQUENCE FROM Roger L. Bagula


      %I A000001
      %S A000001 9,5,4,5,8,34,13,6,5,5,6,17,22,7,5,4,6,11,64,8,5,4,5,9,73,11,6,4,5,7,23,16,6,5,
      4,6,14,32,7,5,4,5,10,550,9,5,4,5,8,36,13,6,4,5,6,17,21,7,5,4,6,12,57,8,5,4,5,
      9,84,11,6,4,5,7,24,16,6,5,4,6,14,30,7,5,4,5,10,273,9,5,4,5,8,39,13,6,4,5,7,18,
      20,7,5,4,6,12,52,8,5,4,5,9,99,11,5,4,5,7,25,16,6,5,5,6,14,28,7,5,4,5,10,183,9,
      5,4,5,8,42,13,6,4,5,7,19,20,7,5,4,6,12,47,8,5,4,5,9,122,10,5,4,5,7,26,15,6,4,
      5,6,15,27,7,5,4,5,10,137,9,5,4,5,8,45,12,6,4,5,7,19,19,7,5,4,6,12,44,8,5,4,5,9
      %N A000001 A 5000 digit fourier projection of the primes.
      %C A000001 I've used a scaled version of the infinite Fourier function: the results are not
      finite as they can be found for every value of n:5000 was just my computer's Mathematica limit.
      %F A000001 e[m_]=Sum[Exp[I*n*m]*Prime[n],{n,1,5000}]
      Table[Floor[Abs[e[m]/5000]],{m,1,200}]
      %t A000001 digits=5000
      c[m_]=Sum[Cos[n*m]*Prime[n],{n,1, digits}];
      s[m_]=Sum[Sin[n*m]*Prime[n],{n,1, digits}];
      e[m_]=c[m]+I*s[m];
      Seq[m_]=Floor[N[Abs[e[m]/digits]]];
      sq=Table[Seq[m],{m,1,200}]
      %O A000001 1
      %K A000001 ,nonn,
      %A A000001 Roger L. Bagula (tftn@...), Sep 13 2003
      RH
      RA 209.179.56.242
      RU
      RI



      --
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      URL : http://home.earthlink.net/~tftn
      URL : http://victorian.fortunecity.com/carmelita/435/




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