MathDB
Problems
Contests
National and Regional Contests
India Contests
Postal Coaching
2015 Postal Coaching
4
4
Part of
2015 Postal Coaching
Problems
(1)
Interesting Recursive Integer Sequence
Source: India Postal Coaching 2015
12/2/2015
The sequence
<
a
n
>
<a_n>
<
a
n
>
is defined as follows,
a
1
=
a
2
=
1
a_1=a_2=1
a
1
=
a
2
=
1
,
a
3
=
2
a_3=2
a
3
=
2
,
a
n
+
3
=
a
n
+
2
a
n
+
1
+
n
!
a
n
,
a_{n+3}=\frac{a_{n+2}a_{n+1}+n!}{a_n},
a
n
+
3
=
a
n
a
n
+
2
a
n
+
1
+
n
!
,
n
≥
1
n \ge 1
n
≥
1
. Prove that all the terms in the sequence are integers.
Sequence
induction
Recurrence
number theory