How Normal Is the MRB Constant?
How Normal Is the MRB Constant?
Move the slider to compute digital expansions, in various bases , of the constant and to digits. The two rows of integers under the row of digits are the frequencies ,,…, of the digits in the base expansions of and . The two rows of decimal numbers are /n,/n,…,/n for and .
b
MRB
π
n
0,1,…,b-1
f
0
f
1
f
b-1
b
MRB
π
f
0
f
1
f
b-1
MRB
π
Normality can be measured by how close the /n are to , say with the function . The closer is to zero, the closer is to being normal in base 10. However, any such numerical evidence is far from a proof.
f
i
{1/b,1/b,…,1/b}
μ(x)=+…+
2
(1/b-/n)
f
0
2
(1/b-/n)
f
b-1
μ(x)
x