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CMIMC Problems
2021 CMIMC
5
5
Part of
2021 CMIMC
Problems
(1)
2021 Team P5
Source:
3/2/2021
Let
N
N
N
be the fifth largest number that can be created by combining
2021
2021
2021
1
1
1
's using addition, multiplication, and exponentiation, in any order (parentheses are allowed). If
f
(
x
)
=
log
2
(
x
)
f(x)=\log_2(x)
f
(
x
)
=
lo
g
2
(
x
)
, and
k
k
k
is the least positive integer such that
f
k
(
N
)
f^k(N)
f
k
(
N
)
is not a power of
2
2
2
, what is the value of
f
k
(
N
)
f^k(N)
f
k
(
N
)
? (Note:
f
k
(
N
)
=
f
(
f
(
⋯
(
f
(
N
)
)
)
)
f^k(N)=f(f(\cdots(f(N))))
f
k
(
N
)
=
f
(
f
(
⋯
(
f
(
N
))))
, where
f
f
f
is applied
k
k
k
times.)Proposed by Adam Bertelli
number theory