On time-bounded incompressibility of compressible strings
Edgar G. Daylight, Wouter M. Koolen and Paul M.B. Vitányi
Information Processing Letters 2008.

Abstract

For every total recursive time bound t, a constant fraction of all compressible (low Kolmogorov complexity) strings is t-bounded incompressible (high time-bounded Kolmogorov complexity); there are infinitely many infinite sequences of which every initial segment is compressible yet t-bounded incompressible; and there is a recursive infinite sequence of which every initial segment is t-bounded incompressible.

[Edit]