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4
4
Part of
2022 Girls in Mathematics Tournament
Problems
(1)
Coprime with 1/2 terms
Source: Brazil EGMO TST 2023 #4
11/10/2022
The sequence of positive integers
a
1
,
a
2
,
a
3
,
…
a_1,a_2,a_3,\dots
a
1
,
a
2
,
a
3
,
…
is brazilian if
a
1
=
1
a_1=1
a
1
=
1
and
a
n
a_n
a
n
is the least integer greater than
a
n
−
1
a_{n-1}
a
n
−
1
and
a
n
a_n
a
n
is coprime with at least half elements of the set
{
a
1
,
a
2
,
…
,
a
n
−
1
}
\{a_1,a_2,\dots, a_{n-1}\}
{
a
1
,
a
2
,
…
,
a
n
−
1
}
. Is there any odd number which does not belong to the brazilian sequence?
number theory