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We present new solutions to the strong explosion problem in a non power lawdensity profi{}le. The unperturbed self similar solutions developed by Sedov,Taylor and Von Neumann describe strong Newtonian shocks propagating into a coldgas with a density profile falling off as $r^{-\omega}$, where$\omega\le\frac{7-\gamma}{\gamma+1}$ (filled type I solutions), and $\gamma$ isthe adiabatic index of the gas. The perturbations we consider are sphericallysymmetric and log periodic with respect to the radius. While the unperturbedsolutions are continuously self similar, the log periodicity of the densityperturbations leads to a discrete self similarity of the perturbations, i.e.,the solution repeats itself up to a scaling at discrete time intervals. Wediscuss these solutions and verify them against numerical integrations of thetime dependent hydrodynamic equations. This is an extension of a previousinvestigation on type II solutions and helps clarifying boundary conditions forperturbations to type I self similar solutions.

Discrete Self Similarity in Filled Type I Strong Explosions