MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2019 India PRMO
24
9's in a Number
9's in a Number
Source: PRMO Leg 2 P24
August 25, 2019
number theory
PRMO
Problem Statement
For
n
≥
1
n \geq 1
n
≥
1
, let
a
n
a_n
a
n
be the number beginning with
n
n
n
9
9
9
's followed by
744
744
744
; eg.,
a
4
=
9999744
a_4=9999744
a
4
=
9999744
. Define
f
(
n
)
=
max
{
m
∈
N
∣
2
m
divides
a
n
}
f(n)=\text{max}\{m\in \mathbb{N} \mid2^m ~ \text{divides} ~ a_n \}
f
(
n
)
=
max
{
m
∈
N
∣
2
m
divides
a
n
}
, for
n
≥
1
n\geq 1
n
≥
1
. Find
f
(
1
)
+
f
(
2
)
+
f
(
3
)
+
⋯
+
f
(
10
)
f(1)+f(2)+f(3)+ \cdots + f(10)
f
(
1
)
+
f
(
2
)
+
f
(
3
)
+
⋯
+
f
(
10
)
.
Back to Problems
View on AoPS