  We prove that twisting any quasi-alternating link $L$ with no gaps in its
Jones polynomial $V_L(t)$ at the crossing where it is quasi-alternating
produces a link $L^{*}$ with no gaps in its Jones polynomial $V_{L^*}(t)$. This
leads us to conjecture that the Jones polynomial of any prime quasi-alternating
link, other than $(2,n)$-torus links, has no gaps. This would give a new
property of quasi-alternating links and a simple obstruction criterion for a
link to be quasi-alternating. We prove that the conjecture holds for
quasi-alternating Montesinos links as well as quasi-alternating links with
braid index 3.
