In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. In a previous paper, we applied it to the Firing Squad Synchronization Problem. In this paper, we show that the approach is not tied to this problem by applying it to the class of Real-Time Sequence Generation problems. We improve in particular on the generation of n3 sequence by using local mappings to obtain millions of 5-state solution, one of them using 58 transitions. It is based on the solution of Kamikawa and Umeo that uses 6 states and 74 transitions. Then, we explain in which sense even bigger classes of problems can be considered.