non-Markov base ten random number generator based on Pi

• To: mathgroup at smc.vnet.net
• Subject: [mg52020] non-Markov base ten random number generator based on Pi
• From: Roger Bagula <tftn at earthlink.net>
• Date: Sun, 7 Nov 2004 01:03:55 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```This result  is an experimental random number generator.
It uses the PSLQ Bailey Pi digits rational polynomial
to generate digits in the 0 to 9 range
using a process that loses information , but generally behaves like the
Pi digits.
It is not Markov, in that there is no previous behavior involved in
calculating the next
random number.

(* Bailey formula with digit drop base 80*)
(* base 10 random number generator that isn't Markov *)
(* use integer seed as the number of digits in to start calculation*)
(* other PSLQ functions of transcendental numbers could be used to do
this same kind of random number*)
f[n_]=Floor[Mod[80^n*(4/(8*n+1)-2/(8*n+4)-1/(8*n+5)-1/(8*n+6))/16^n,10]]
Digits=4000;rdpi=Table[f[n],{n,0,Digits}];
c1=Drop[FoldList[Plus,0,Sign[Drop[rdpi,1]-Drop[rdpi,-1]]],1];
ListPlot[c1,PlotJoined->True];
(* Rowe Count*)
d1=Flatten@{0,Length/@Split[Sort@c1], 0}
Dimensions[d1][[1]]
ListPlot[d1,PlotJoined->True];

a=Table[f[n],{n,0,200}]

{3,0,1,2,7,5,0,7,7,7,4,9,2,0,3,9,9,8,2,0,5,6,3,0,9,3,6,6,4,8,7,2,3,8,4,3,2,1,

1,2,4,7,5,8,5,0,8,4,3,2,6,6,7,4,6,9,6,5,9,5,4,1,8,9,7,2,8,5,4,3,0,3,3,0,5,7,

6,2,0,1,4,0,1,6,9,7,2,0,4,0,1,8,1,8,8,2,9,3,1,4,4,3,0,1,3,4,0,5,8,8,9,6,8,3,

5,1,5,5,4,5,1,4,6,5,7,1,9,8,8,2,3,1,6,0,8,7,1,6,7,6,2,5,3,5,7,7,7,2,7,6,1,4,

7,4,9,3,4,8,3,5,5,5,9,3,0,8,4,8,5,8,4,0,9,8,3,8,2,6,7,0,5,8,9,3,7,8,4,2,9,0,
1,2,6,1,2,9,1,7,0,7,6}
Respectfully, Roger L. Bagula