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Baltic Way
2023 Baltic Way
1
Interesting sequence
Interesting sequence
Source: Baltic Way 2023/1
November 11, 2023
algebra
Problem Statement
Find all strictly increasing sequences of positive integers
a
1
,
a
2
,
…
a_1, a_2, \ldots
a
1
,
a
2
,
…
with
a
1
=
1
a_1=1
a
1
=
1
, satisfying
3
(
a
1
+
a
2
+
…
+
a
n
)
=
a
n
+
1
+
…
+
a
2
n
3(a_1+a_2+\ldots+a_n)=a_{n+1}+\ldots+a_{2n}
3
(
a
1
+
a
2
+
…
+
a
n
)
=
a
n
+
1
+
…
+
a
2
n
for all positive integers
n
n
n
.
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