How can one construct a Kurtz random sequence that's not Martin-Löf random?
I'm also interested in the paper that included the first of such constructions. I suspect it was in Kurtz's dissertation, but it's not very accessible.
I'd be grateful for you help in this matter.
Check out Nies' Computability and Randomness, section 3.5. There he shows that every weakly 1-generic sequence is Kurtz random (Fact 3.5.4) and that weakly 1-generics fail the law of large numbers (Proposition 3.5.5). Since every Martin-Löf random satisfies the law of large numbers, one need only construct a weakly 1-generic.