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All-Russian Olympiad
1985 All Soviet Union Mathematical Olympiad
405
ASU 405 All Soviet Union MO 1985 a_{2n}=a_n, a_{4n+1}=1, a_{4n+3}=0
ASU 405 All Soviet Union MO 1985 a_{2n}=a_n, a_{4n+1}=1, a_{4n+3}=0
Source:
August 5, 2019
periodical
Sequence
Problem Statement
The sequence
a
1
,
a
2
,
.
.
.
,
a
k
,
.
.
.
a_1, a_2, ... , a_k, ...
a
1
,
a
2
,
...
,
a
k
,
...
is constructed according to the rules:
a
2
n
=
a
n
,
a
4
n
+
1
=
1
,
a
4
n
+
3
=
0
a_{2n} = a_n,a_{4n+1} = 1,a_{4n+3} = 0
a
2
n
=
a
n
,
a
4
n
+
1
=
1
,
a
4
n
+
3
=
0
Prove that it is non-periodical sequence.
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