  A search is reported for high-mass hadronic resonances that decay to a parton
and a Lorentz-boosted resonance, which in turn decays into a pair of partons.
The search is based on data collected with the CMS detector at the LHC in
proton-proton collisions at $\sqrt{s} =$ 13 TeV, corresponding to an integrated
luminosity of 138 fb$^{-1}$. The boosted resonance is reconstructed as a single
wide jet with substructure consistent with a two-body decay. The high-mass
resonance is thus considered as a dijet system. The jet substructure
information and the kinematic properties of cascade resonance decays are
exploited to disentangle the signal from the large quantum chromodynamics
multijet background. The dijet mass spectrum is analyzed for the presence of
new high-mass resonances, and is found to be consistent with the standard model
background predictions. Results are interpreted in a warped extra dimension
model where the high-mass resonance is a Kaluza-Klein gluon, the boosted
resonance is a radion, and the final state partons are all gluons. Limits on
the production cross section are set as a function of the Kaluza-Klein gluon
and radion masses. These limits exclude at 95% confidence level models with
Kaluza-Klein gluon masses in the range from 2.0 to 4.3 TeV and radion masses in
the range from 0.20 to 0.74 TeV. By exploring a novel experimental signature,
the observed limits on the Kaluza-Klein gluon mass are extended by up to about
1 TeV compared to previous searches.
