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Chile Contests
Chile National Olympiad
2016 Chile National Olympiad
1
1
Part of
2016 Chile National Olympiad
Problems
(1)
a_n=1234567891011 ...n is not divisible by 3 (Chile 2016 L2 P1)
Source:
10/22/2022
The natural number
a
n
a_n
a
n
is obtained by writing together and ordered, in decimal notation , all natural numbers between
1
1
1
and
n
n
n
. So we have for example that
a
1
=
1
a_1 = 1
a
1
=
1
,
a
2
=
12
a_2 = 12
a
2
=
12
,
a
3
=
123
a_3 = 123
a
3
=
123
,
.
.
.
. . .
...
,
a
11
=
1234567891011
a_{11} = 1234567891011
a
11
=
1234567891011
,
.
.
.
...
...
. Find all values of
n
n
n
for which
a
n
a_n
a
n
is not divisible by
3
3
3
.
number theory
divisible