# 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