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MathGroup Archive 2004

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Re: bimodal ditribution form counting signs of Pi digits differences

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51733] Re: bimodal ditribution form counting signs of Pi digits differences
  • From: Roger Bagula <tftn at earthlink.net>
  • Date: Sun, 31 Oct 2004 01:16:21 -0500 (EST)
  • References: <clst68$3nf$1@smc.vnet.net>
  • Reply-to: tftn at earthlink.net
  • Sender: owner-wri-mathgroup at wolfram.com

Null hypothesis: the digits of Pi are random.
To check make up a random set of base 10 digits using Mathematica
using:
 Random[Integer,{0,9}]
I picked a seed off the top of my head.
The result is a revolting development.
A trimodal distribution of noise pushed way positive.
The Pi digits behave more like an "ideal" probablity
than the Mathematica random!
Anybody see what I did wrong?
Dr. Bob you always have an opinion, ha, ha...

(* random digit array base 10*)
SeedRandom[123]
a=Table[Random[Integer,{0,9}],{n,1,2000}];
b=Table[Sum[Sign[a[[m+1]]-a[[m]]],{m,1,n}],{n,1,Dimensions[a][[1]]-1}];
ListPlot[b,PlotJoined->True]
(* distribution of the noise that results*)
Max[b]
Min[b]
c=Table[Count[b,m],{m,Min[b]-1,Max[b]+1}]
ListPlot[c,PlotJoined->True]


Roger Bagula wrote:

>This program  is real slow on my machine.
>Show a lean toward positive differences that is "slight" at 2000 digits. 
>
>Digits=2000
>$MaxExtraPrecision = Digits
>(* Sum of the sign of the differences between the first 2000 digits of Pi*)
>f[m_]=Sum[Sign[Floor[Mod[10^(n+1)*Pi,10]]-Floor[Mod[10^n*Pi,10]]],{n,0,m}]
>a=Table[{n,f[n]},{n,0,Digits-1}];
>ListPlot[a,PlotJoined->True]
>b=Table[a[[n]][[2]],{n,1,Dimensions[a][[1]]}];
>(* distribution of the noise that results*)
>c=Table[Count[b,m],{m,-12,12}]
>ListPlot[c,PlotJoined->True]
>
>Respectfully, Roger L. Bagula
>tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
>alternative email: rlbtftn at netscape.net
>URL :  http://home.earthlink.net/~tftn
>
>  
>

-- 
Respectfully, Roger L. Bagula
tftn at earthlink.net, 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
alternative email: rlbtftn at netscape.net
URL :  http://home.earthlink.net/~tftn



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