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

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  • Roger Bagula
    ... Subject: SEQ FROM Roger L. Bagula Date: Sun, 14 Sep 2003 17:04:22 -0400 (EDT) From: Reply-To: tftn@earthlink.net To:
    Message 1 of 1 , Sep 14, 2003
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      -------- Original Message --------
      Subject: SEQ FROM Roger L. Bagula
      Date: Sun, 14 Sep 2003 17:04:22 -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
      containing the sequence you submitted.

      All greater than and less than signs have been replaced by their html
      equivalents. They will be changed back when the message is processed.

      This copy is just for your records. No reply is expected.
      Subject: NEW SEQUENCE FROM Roger L. Bagula


      %I A000001
      %S A000001 34256905988,13833711045,3161243909,867446001,79422563,2390757,278055,8098,104,
      1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
      0,0
      %N A000001 A scaled integer projection of the Primes onto a Hermite Hilbert space of orthogonal functions by a sum.
      %C A000001 This result is scaled so the smallest integer greater than zero is one. It is
      the most number of basis functions (25) my computer will calculate before crashing. This result was suggested by finding that:
      Sum[Exp[-n^2]*Prime[n],{n,1,infinity}]=0.791323635928514
      to 200 decimals: that is it is finite and rational.
      %F A000001 Hermite recursive Polynomial from Jahnke and Emde: "Tables of Functions", page 32
      H[n_Integer?Positive] :=H[n] =m*H[n-1] -(n-1)* H[n-2]
      H[0] = 1
      H[1] = m
      Table[Abs[Floor[Sum[H[n]**Exp[-m^2/2]*Prime[n],{n,1,25}]/5^5]],{m,1,50}]

      %t A000001 H[n_Integer?Positive] :=H[n] =m*H[n-1] -(n-1)* H[n-2]
      H[0] = 1
      H[1] = m
      digits=25
      h[m_]=Sum[H[n]*Exp[-m^2/2]*Prime[n+1],{n,0, digits}];
      Seq[m_]=Floor[N[h[m]/(5*digits^2)]];
      sq=Table[Seq[m],{m,1,50}]
      Abs[sq]
      %O A000001 0
      %K A000001 ,nonn,
      %A A000001 Roger L. Bagula (tftn@...), Sep 14 2003
      RH
      RA 209.178.174.68
      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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