Sequences Containing No 3-Term Arithmetic Progressions
Sequences Containing No 3-Term Arithmetic Progressions
A subsequence of the sequence $(1,2,...,n)$ is called a 3-$AP$-free sequence if it does not contain any three term arithmetic progression. By $r(n)$ we denote the length of the longest such 3-$AP$-free sequence. The exact values of the function $r(n)$ were known, for $n\leq 27$ and $41\leq n \leq 43$. …