How Normal Is the MRB Constant?

0	1


MRB
1	0
1.0000	0.0000

μ(MRB)
0.7071


π
1	0
1.0000	0.0000

μ(π)
0.7071

Move the slider to compute digital expansions, in various bases

b

, of the

MRB

constant and

π

to

n

digits. The two rows of integers under the row of digits

0,1,…,b-1

are the frequencies

f

0

,

f

1

,…,

f

b-1

of the digits in the base

b

expansions of

MRB

and

π

. The two rows of decimal numbers are

f

0

/n,

f

1

/n,…,

f

b-1

/n

for

MRB

and

π

.

Normality can be measured by how close the

f

i

/n

are to

{1/b,1/b,…,1/b}

, say with the function

μ(x)=

2

(1/b-

f

0

/n)

+…+

2

(1/b-

f

b-1

/n)

. The closer

μ(x)

is to zero, the closer

x

is to being normal in base 10. However, any such numerical evidence is far from a proof.