  Hermann Minkowski introduced a function in 1904 which maps quadratic
irrational numbers to rational numbers and this function is now known as
Minkowski's question mark function since Minkowski used the notation $?(x)$.
This function is a distribution function on $[0,1]$ which defines a singular
continuous measure with support $[0,1]$. Our interest is in the (monic)
orthogonal polynomials $(P_n)_{n \in \mathbb{N}}$ for the Minkowski measure and
in particular in the behavior of the recurrence coefficients of the three term
recurrence relation. We will give some numerical experiments using the
discretized Stieltjes-Gautschi method with a discrete measure supported on the
Minkowski sequence. We also explain how one can compute the moments of the
Minkowski measure and compute the recurrence coefficients using the Chebyshev
algorithm.
