Komornik-Loreti Constant

Author

Eric W. Weisstein
April 14, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Komornik-LoretiConstant.nb.

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

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

Value

Sum[((Mod[DigitCount[n,2,1],2])/(q^n)),{n,∞}]

FindRoot[Sum[((Mod[DigitCount[n,2,1],2])/(q^n)),{n,2000}]-1,{q,1.7},WorkingPrecision->100]

FindRoot[Sum[((Mod[DigitCount[n,2,1],2])/(q^n)),{n,5000}]-1,{q,1.7},WorkingPrecision->1000]

FindRoot[Sum[((Mod[DigitCount[n,2,1],2])/(q^n)),{n,10^4}]-1,{q,1.7},WorkingPrecision->1000]

V7

Product[1-(1/(q^(2^k))),{k,0,∞}]

p[q_]=Product[1-(1/(q^(2^k))),{k,0,15}];

Plot[p[q]-((((1-(1/q)))^(-1))-2),{q,1.5,2}]

FindRoot[p[q]==((((1-(1/q)))^(-1))-2),{q,1.8},WorkingPrecision->30]

FindRoot[p[q]==((((1-(1/q)))^(-1))-2),{q,1.8},WorkingPrecision->100]//Timing