MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN M Problems
16
16
Part of
PEN M Problems
Problems
(1)
M 16
Source:
5/25/2007
Define a sequence
{
a
i
}
\{a_i\}
{
a
i
}
by
a
1
=
3
a_1=3
a
1
=
3
and
a
i
+
1
=
3
a
i
a_{i+1}=3^{a_i}
a
i
+
1
=
3
a
i
for
i
≥
1
i\geq 1
i
≥
1
. Which integers between
00
00
00
and
99
99
99
inclusive occur as the last two digits in the decimal expansion of infinitely many
a
i
a_i
a
i
?
Recursive Sequences