Sequences of Integers Avoiding 3-term Arithmetic Progressions

Arun Sharma

Abstract


The optimal length $r(n)$ of a sequence in $[1, n]$ containing no $3$-term arithmetic progression is determined for several new values of $n$ and some results relating to the subadditivity of $r$ are obtained.  We also prove a particular case of a conjecture of Szekeres.


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