Let $M = w_0w_1... \in \{0,1\}^*$.
For any computable function $f$ define $M_f = w_{f(0)}w_{f(1)}...$

Let for any computable function $f$ with infinitely range of values  there is continuous
computable mapping between $M_f$ and $M$
(we can reestablish $M$ by its any computable subsequence)

Is it possible that $M$ is non-computable?