  The Sturm sequence is generated by a pair of polynomials $P(x)$ and $P'(x)$,
where $P(x)$ is assumed to have simple real roots. Euclidean algorithm
generates then a finite sequence of polynomials orthogonal on the grid $x_s$ of
roots of the polynomial $P(x)$. This algorithm can be exploited in order to
find the number of roots of the polynomial $P(x)$ inside a given interval. We
consider the "inverse" problem: what is the explicit system of orthogonal
polynomials generated by the prescribed grid $x_s$ of "classical" type. The
main results are the following. The generic linear grid generates a special
case of the Hahn polynomials. The quadratic grids $x_s=x(s+1)$ and $x_s=s(s+2)$
correspond to two special cases of the Racah polynomials. The generic
exponential grid is related to a special case of the q-Hahn polynomials.
Finally, we show that two special trigonometric grids are related to the
Chebyshev polynomials of the first and second kind.
