Delian Constant

Author

Eric W. Weisstein
September 28, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Value

delian=ExactConstant["Delian constant"]

Numerical

N[delian,20]

Algebraic Degree

AlgebraicDegree[delian]

Continued Fraction

ContinuedFraction[delian,50]

{10,2,1,4,12,2,3,2,1,3,4,1,1,2,14,3,12,1,15,3,1,4,534,1,1,5,1,1,121,1,2,2,4,10,3,2,2}

BBP-Type Formulas

Search

<<Utilities`Simplify`

Monitor[Do[If[(b=FindBasis[2^(1/3),-3^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,1}],{-3^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-3^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,2,2}],{-3^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-3^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,3,3}],{-3^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-2^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,1}],{-2^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-2^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,2,2}],{-2^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-2^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,3,3}],{-2^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-1,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,0,0},{n,64},{p,1}],{-1,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-1,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,0,0},{n,64},{p,2,2}],{-1,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),-1,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,0,0},{n,64},{p,3,3}],{-1,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),1,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,0,0},{n,64},{p,2,2}],{1,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),1,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,0,0},{n,64},{p,3,3}],{1,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),2^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,1}],{2^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),2^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,2,2}],{2^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),2^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,3,3}],{2^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),3^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,1}],{3^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),3^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,2,2}],{3^k,n,p}];//Timing

Monitor[Do[If[(b=FindBasis[2^(1/3),3^k,n,BasisPower->p,WorkingPrecision->300])=!={},Print[b]],{k,16},{n,64},{p,3,3}],{3^k,n,p}];//Timing