Feynman Point

Author

Eric W. Weisstein
April 16, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/FeynmanPoint.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/FeynmanPoint.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

pi=RealDigits[Pi,10,10^6][[1]];//Timing

Strings of Digits

Table[If[#=={},{},#[[1]]-1]&[Position[Partition[pi,n,1],Table[0,{n}],1,1]],{n,6}]//Flatten//Timing

Table[If[#=={},{},#[[1]]-1]&[Position[Partition[pi,n,1],Table[9,{n}],1,1]],{n,8}]//Flatten//Timing

666

Position[Partition[pi,3,1],{6,6,6},1,10]-1//Flatten

012345678

Position[Partition[pi,9,1],Range[0,8]]

Position[Partition[pi,9,1],Range[9]]

{StringPosition[pi,"012345678",1],StringPosition[pi,"123456789",1]}

Digits Counts

Length/@Split[Sort[pi]]

Plus@@%

High Water Marks

pi=ContinuedFraction[Pi,10000];
Do[
Print[i," Digits:"];
dig=Select[pi,i-1≤Log[10,#]<i&,120];
Print[dig];
Print["which occur at"];
pos=Sort[Flatten[Position[pi,#,1]&/@Union[dig]]]-1;
Print[If[Length[pos]<120,pos,Take[pos,120]]],
{i,1,4}]

pi=ContinuedFraction[Pi,100000];
Do[
Print[i," Digits:"];
dig=Select[pi,i-1≤Log[10,#]<i&,100];
Print[dig];
Print["which occur at"];
pos=Sort[Flatten[Position[pi,#,1]&/@Union[dig]]]-1;
Print[If[Length[pos]<100,pos,Take[pos,100]]],
{i,4,4}]