Pickover's Sequence

Author

Eric W. Weisstein
January 17, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/PickoversSequence.nb.

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

©2006 Wolfram Research, Inc. except for portions noted otherwise

E in Pi

edig=StringJoin@@@Reverse[NestList[Most,ToString/@RealDigits[E,10,10][[1]],9]]

(10^7)

pidig=StringDrop[ToString[N[Pi,10^7+1]],2];//Timing

pidig=StringJoin@@(ToString/@RealDigits[Pi,10,10^7,-1][[1]]);//Timing

Flatten[If[#==={},{},#[[1,1]]]&/@(StringPosition[pidig,#,1]&/@edig)]

(10^8)

pidig=StringDrop[ToString[N[Pi,10^8+1]],2];//Timing

Flatten[If[#==={},{},#[[1,1]]]&/@(StringPosition[pidig,#,1]&/@edig)]

Pi in E

pidig=StringJoin@@@Reverse[NestList[Most,ToString/@RealDigits[Pi,10,10][[1]],9]]

(10^7)

edig=StringDrop[ToString[N[E,10^7+1]],2];//Timing

Flatten[If[#==={},{},#[[1,1]]]&/@(StringPosition[edig,#,1]&/@pidig)]

(10^8)

edig=StringDrop[ToString[N[E,10^8+1]],2];//Timing

Flatten[If[#==={},{},#[[1,1]]]&/@(StringPosition[edig,#,1]&/@pidig)]

5 × (10^8)

edig=StringDrop[ToString[N[E,5 10^8+1]],2];//Timing

Flatten[If[#==={},{},#[[1,1]]]&/@(StringPosition[edig,#,1]&/@pidig)]