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Putnam
1985 Putnam
A4
A4
Part of
1985 Putnam
Problems
(1)
Putnam 1985 A4
Source:
8/5/2019
Define a sequence
{
a
i
}
\left\{a_{i}\right\}
{
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
?
Putnam