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Duffin's Sequence for Pi

​
approximation of π
x
3.14159
length of Duffin's sequence:
70
π - x =
0.
0123456
0123456
0123456
0123456
0123456
0123456
0123456
0123456
0123456
0123456
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?
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