  In this paper we study subsequences of random numbers. In Kamae (1973),
selection functions that depend only on coordinates are studied, and their
necessary and sufficient condition for the selected sequences to be normal
numbers is given. In van Lambalgen (1987), an algorithmic analogy to the
theorem is conjectured in terms of algorithmic randomness and Kolmogorov
complexity. In this paper, we show different algorithmic analogies to the
theorem.
