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2010 Cono Sur Olympiad
6
6
Part of
2010 Cono Sur Olympiad
Problems
(1)
Infinite sequence of integers
Source: Cono Sur 2010 #6
11/17/2015
Determine if there exists an infinite sequence
a
0
,
a
1
,
a
2
,
a
3
,
.
.
.
a_0, a_1, a_2, a_3,...
a
0
,
a
1
,
a
2
,
a
3
,
...
of nonegative integers that satisfies the following conditions: (i) All nonegative integers appear in the sequence exactly once. (ii) The succession
b
n
=
a
n
+
n
,
b_n=a_{n}+n,
b
n
=
a
n
+
n
,
,
n
≥
0
n\geq0
n
≥
0
, is formed by all prime numbers and each one appears exactly once.
number theory
cono sur