Re: bimodal ditribution form counting signs of Pi digits differences

• To: mathgroup at smc.vnet.net
• Subject: [mg51773] Re: bimodal ditribution form counting signs of Pi digits differences
• From: Roger Bagula <tftn at earthlink.net>
• Date: Mon, 1 Nov 2004 02:53:28 -0500 (EST)
• References: <clst68\$3nf\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```A second crack at a null hypothesis using an
independent pseudorandom generator.
Results from this generator are more variable than the Mathematica built in
as you can change both the seed start number and the irrational it is
based on.
It too gives a different result than the Pi digits.

Mathematica code:
Clear[r,s,a,c1,d1]
s=5
(*Pseudorandom number algorithm from Forcasting on Your
Microcomuter,nickell, tab books, 1983*)
SeedRandom[123]
r[n_Integer]:=r[n]=Mod[(E+r[n-1])^s,1]
r[0]=Random[]
digits =50000
a=Table[Mod[Floor[10*r[n]],10],{n,1,digits}];
c1=Drop[FoldList[Plus,0,Sign[Drop[a,1]-Drop[a,-1]]],1];
ListPlot[c1,PlotJoined->True];
(* Rowe Count*)
d1=Flatten@{0,Length/@Split[Sort@c1], 0}
ListPlot[d1,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
>alternative email: rlbtftn at netscape.net
>
>
>

--
Respectfully, Roger L. Bagula