Intuitionistic sequential compactness?

Perhaps because the classical notion of sequential compactness fails to apply constructively even to {0,1}, Brouwer and his successors have paid little attention to the possibility of a constructive counterpart that is classically equivalent to sequential compactness and has serious potential for applications in analysis. We discuss such a notion - the anti-Specker property - and its equivalence, over Bishop-style constructive mathematics, to Brouwer's fan theorem for c-bars.