  In a prequential approach to algorithmic randomness, probabilities for the
next outcome can be forecast `on the fly' without the need for fully specifying
a probability measure on all possible sequences of outcomes, as is the case in
the more standard approach. We take the first steps in allowing for probability
intervals instead of precise probabilities in this prequential approach, based
on ideas from our earlier imprecise-probabilistic and martingale-theoretic
account of algorithmic randomness. We define what it means for an infinite
sequence $(I_1,x_1,I_2,x_2,\dots)$ of successive interval forecasts $I_k$ and
subsequent binary outcomes $x_k$ to be random. We compare the resulting
prequential randomness notion with the more standard one, and investigate where
both randomness notions coincide, as well as where their properties correspond.
