Duffin's Sequence for Pi

approximation of π

x

3.14159

length of Duffin's sequence:

70

π - x =

0.

2

7

Duffin's sequence for positive number

x

is defined by:

duffin(x,n)=⌊7(nx-⌊nx⌋)⌋

,

where

⌊y⌋

is the integer part of

y

(or the floor of

y

). For a given

x

,

duffin(x,n)

is a sequence of digits 0, 1, 2, ..., 6.

If

x=π

, we get 0123456012345601234560123456…. Does this sequence have period 0123456?