MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - Middle School Tournaments
LMT
2020 LMT Spring
16
Spring 2020 Team Round Problem 16
Spring 2020 Team Round Problem 16
Source:
August 22, 2020
Problem Statement
For non-negative integer
n
n
n
, the function
f
f
f
is given by
f
(
x
)
=
{
x
2
if
n
is even
x
−
1
if
n
is odd.
f(x)=\begin{cases} \frac{x}{2} & \text{if $n$ is even} \\ x-1 & \text{if $n$ is odd.} \end{cases}
f
(
x
)
=
{
2
x
x
−
1
if
n
is even
if
n
is odd.
Furthermore, let
h
(
n
)
h(n)
h
(
n
)
be the smallest
k
k
k
for which
f
k
(
n
)
=
0
f^k(n)=0
f
k
(
n
)
=
0
. Compute
∑
n
=
1
1024
h
(
n
)
.
\sum_{n=1}^{1024} h(n).
n
=
1
∑
1024
h
(
n
)
.
Back to Problems
View on AoPS