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 ($pp to ellell jj$) 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.
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