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)

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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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