A colouring problem

Find the least natural number $n$ $(n\geq 3)$ with the following property: for any colouring of $n$ distinct points $A_1, A_2, \dots , A_n$ in two colours, there exist three points $A_i, A_j, A_{2j-i}$ $(1\leq i < 2j-i \leq n)$ which are coloured in the same colour.