Chaitin's Constant

Author

Eric W. Weisstein
March 3, 2009

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

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

©2009 Wolfram Research, Inc. except for portions noted otherwise

Digits

Calude et al. (2002)

Ω={0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,0,0,0,1,1,0,1,0,0,0,1,1,1,1,1,1,0,0,1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0,0,0};

Calude and Dinneen 2007

(Subscript[Ω, U16])={0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,1,0,1,1,1,0};

(Subscript[Ω, U2])={0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0,1,0,0,1,1,1,0,1,1,1,0,0,0,0,1,1,1,1,1,0,1,0};

Length/@{Ω,(Subscript[Ω, U16]),(Subscript[Ω, U2])}

StringJoin[ToString/@#]&/@{Ω,(Subscript[Ω, U16]),(Subscript[Ω, U2])}//Column

N[FromDigits[{#,0},2],{200,-Log[10,2^-Length[#]]}]&/@{Ω,(Subscript[Ω, U16]),(Subscript[Ω, U2])}//Column