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Putnam
1991 Putnam
B1
Sequence
Sequence
Source: Putnam 1991
May 23, 2006
Problem Statement
For each integer
n
≥
0
n\geq0
n
≥
0
, let
S
(
n
)
=
n
−
m
2
S(n)=n-m^2
S
(
n
)
=
n
−
m
2
, where
m
m
m
is the greatest integer with
m
2
≤
n
m^2\leq n
m
2
≤
n
. Define a sequence by
a
0
=
A
a_0=A
a
0
=
A
and
a
k
+
1
=
a
k
+
S
(
a
k
)
a_{k+1}=a_k+S(a_k)
a
k
+
1
=
a
k
+
S
(
a
k
)
for
k
≥
0
k\geq0
k
≥
0
. For what positive integers
A
A
A
is this sequence eventually constant?
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