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Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
1987 AMC 12/AHSME
29
29
Part of
1987 AMC 12/AHSME
Problems
(1)
1987 AMC 12 #29 - Recursive Sequence
Source:
1/1/2012
Consider the sequence of numbers defined recursively by
t
1
=
1
t_1=1
t
1
=
1
and for
n
>
1
n>1
n
>
1
by
t
n
=
1
+
t
(
n
/
2
)
t_n=1+t_{(n/2)}
t
n
=
1
+
t
(
n
/2
)
when
n
n
n
is even and by
t
n
=
1
t
(
n
−
1
)
t_n=\frac{1}{t_{(n-1)}}
t
n
=
t
(
n
−
1
)
1
when
n
n
n
is odd. Given that
t
n
=
19
87
t_n=\frac{19}{87}
t
n
=
87
19
, the sum of the digits of
n
n
n
is
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
15
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
17
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
19
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
21
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
23
<span class='latex-bold'>(A)</span>\ 15 \qquad<span class='latex-bold'>(B)</span>\ 17 \qquad<span class='latex-bold'>(C)</span>\ 19 \qquad<span class='latex-bold'>(D)</span>\ 21 \qquad<span class='latex-bold'>(E)</span>\ 23
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
15
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
17
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
19
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
21
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
23
AMC