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Baltic Way
2006 Baltic Way
1
classic sequence
classic sequence
Source: baltic way, 2006
May 1, 2007
Problem Statement
For a sequence
(
a
n
)
n
≥
1
(a_{n})_{n\geq 1}
(
a
n
)
n
≥
1
of real numbers it is known that
a
n
=
a
n
−
1
+
a
n
+
2
a_{n}=a_{n-1}+a_{n+2}
a
n
=
a
n
−
1
+
a
n
+
2
for
n
≥
2
n\geq 2
n
≥
2
. What is the largest number of its consecutive elements that can all be positive?
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