We searched for Tc in a sample of long period variables selected by stellar luminosity derived from Hipparcos parallaxes. Tc, as an unstable s-process element, is a good indicator for the evolutionary status of stars on the asymptotic giant branch (AGB). In this paper we study the occurrence of Tc as a function of luminosity to provide constraints on the minimum luminosity for the third dredge up as estimated from recent stellar evolution models. A large number of AGB stars above the estimated

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... heoretical limit for the third dredge up are found not to show Tc. We confirm previous findings that only a small fraction of the semiregular variables show Tc lines in their spectra. Contrary to earlier results by Little et al. (1987) we find also a significant number of Miras without Tc. The presence and absence of Tc is discussed in relation to the mass distribution of AGB stars. We find that a large fraction of the stars of our sample must have current masses of less than 1.5 M_. Combining our findings with stellar evolution scenarios we conclude that the fraction of time a star is observed as a SRV or a Mira is dependent on its mass.