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16
M 16
M 16
Source:
May 25, 2007
Recursive Sequences
Problem Statement
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
?
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