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First occurrence of a decimal digit
ID: first-occurrence-of-a-decimal-digit
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First occurrence of a decimal digit
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
Under uniform
length
on
[
0
,
1
]
, the
position
K
of the
first
occurrence of
a
fixed
decimal
digit has
Pr
(
K
=
k
)
=
10
1
(
10
9
)
k
−
1
.
(1)
The
set
of expansions in which the digit never occurs has
length
zero, and
E
K
=
∑
k
≥
1
10
k
(
10
9
)
k
−
1
=
10.
(2)
Total
articles
:
1
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