We measured the K -series X-rays of the K−p exotic atom in the SIDDHARTA experiment with a gaseous hydrogen target of 1.3 g/l, which is about 15 times the ρSTP of hydrogen gas. At this density, the absolute yields of kaonic X-rays, when a negatively charged kaon stopped inside the target, were determined to be for Kα and for all the K -series transitions Ktot. These results, together with the KEK E228 experiment results, confirm for the first time a target density dependence of the yield predicted by the cascade models, and provide valuable information to refine the parameters used in the cascade models for the kaonic atoms.