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|a_n-n^2 | < n/2, arithmetic progression

Source: Argentina 2004 OMA L3 p6

May 12, 2024
Arithmetic Progressionalgebraarithmetic sequence

Problem Statement

Decide if it is possible to generate an infinite sequence of positive integers ana_n such that in the sequence there are no three terms that are in arithmetic progression and that for all nn \left |a_n-n^2\right | <\frac{n}{2}.
Clarification: Three numbers aa, bb, cc are in arithmetic progression if and only if 2b=a+c2b=a+c.
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