Given any oracle, , we construct a basic sequence , computable in the jump of , such that no -computable real is -distribution-normal. A corollary to this is that there is a basic sequence with respect to which no real is distribution-normal. As a special case, there is a limit computable sequence relative to which no computable real is distribution-normal.
"Normal Numbers and Limit Computable Cantor Series." Notre Dame J. Formal Logic 58 (2) 215 - 220, 2017. https://doi.org/10.1215/00294527-2017-0004