its inverse square falloff for radio energy dissipation so I'd say it goes away really really quickly. also you have the problem of overcoming Sun's 'blaring' background signal unless you took your signal generator and placed it outside of oort cloud or further.
Another idea is to put a mylar parabolic mirror behind the bombs. A very short burst of light is going to get focused in a beam before the mylar is vapourised. Maybe someone smart here could calculate exactly how short the beam would be.
That short burst could be in itself a significant signature. What, in nature, could produce such a short concentrated energy burst?
problem with such a tight-beam is you have to be in direct line of sight for it to be seen. which means a very small number of receivers civilization can ever know, that is exact opposite of the goals of a 'lighthouse'. perhaps something that sweeps around at regular intervals with some precession thrown in for coverage, that makes it closer to GP's comment about neutron star emitting prime numbers.
oort cloud is just a stand-in for generating enough parallax in the signal from sun. further out you go better it would be. in fact it just occurred to me that you could just launch an emitter perpendicular to galactic plane with enough velocity that it bobbles up and down say 3x over what a normal star would and it would serve as a galactic lighthouse for intelligent civilization.
