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CentroAmerican
2002 CentroAmerican
3
3
Part of
2002 CentroAmerican
Problems
(1)
Sequence
Source: Central American Olympiad 2002, problem 3
12/30/2009
For every integer
a
>
1
a>1
a
>
1
an infinite list of integers is constructed
L
(
a
)
L(a)
L
(
a
)
, as follows:
a
a
a
is the first number in the list
L
(
a
)
L(a)
L
(
a
)
. Given a number
b
b
b
in
L
(
a
)
L(a)
L
(
a
)
, the next number in the list is b\plus{}c, where
c
c
c
is the largest integer that divides
b
b
b
and is smaller than
b
b
b
. Find all the integers
a
>
1
a>1
a
>
1
such that
2002
2002
2002
is in the list
L
(
a
)
L(a)
L
(
a
)
.