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2024-IMOC
A3
An easy sequence but casework
An easy sequence but casework
Source: Own
August 3, 2024
Sequence
Integer sequence
Problem Statement
Find all infinite integer sequences
a
1
,
a
2
,
…
a_1,a_2,\ldots
a
1
,
a
2
,
…
satisfying
a
n
+
2
a
n
+
1
=
a
n
+
1
+
a
n
a_{n+2}^{a_{n+1}}=a_{n+1}+a_n
a
n
+
2
a
n
+
1
=
a
n
+
1
+
a
n
holds for all
n
≥
1
n\geq 1
n
≥
1
. Define
0
0
=
1
0^0=1
0
0
=
1
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