       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: Sat, 30 Oct 2004 03:49:05 -0400 (EDT)
• References: <clst68\$3nf\$1@smc.vnet.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
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}];
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]][],{n,1,Dimensions[a][]}];
>(* distribution of the noise that results*)
>c=Table[Count[b,m],{m,-12,12}]
>ListPlot[c,PlotJoined->True]
>
>Respectfully, Roger L. Bagula
>alternative email: rlbtftn at netscape.net
>
>
>

--
Respectfully, Roger L. Bagula