Školjka

%V0 We are given a fixed point on the circle of radius $1$, and going from this point along the circumference in the positive direction on curved distances $0, 1, 2, \ldots$ from it we obtain points with abscisas $n = 0, 1, 2, .\ldots$ respectively. How many points among them should we take to ensure that some two of them are less than the distance $\frac 15$ apart ?