  We investigate the search for heavy Majorana neutrinos stemming from a
composite model scenario at the upcoming LHC Run II at a center of mass energy
of 13 TeV. While previous studies of the composite Majorana neutrino were
focussed on gauge interactions via magnetic type transition coupling between
ordinary and heavy fermions (with mass $m^*$) here we complement the composite
model with contact interactions at the energy scale $\Lambda$ and we find that
the production cross sections are dominated by such contact interactions by
roughly two/three orders of magnitude. This mechanism provides therefore very
interesting rates at the prospected luminosities. We study the same sign
di-lepton and di-jet signature ($pp \to \ell\ell jj$) and perform a fast
detector simulation based on Delphes. We compute 3$\sigma$ and 5$\sigma$
contour plots of the statistical significance in the parameter space
($\Lambda,m^*$). We find that the potentially excluded regions at $\sqrt{s}
=13$ TeV are quite larger than those excluded so far at Run I considering
searches with other signatures.
