Submitted to JHEP. All figures and tables can be found at http://cms-results.web.cern.ch/cms-results/public-results/publications/FSQ-16-002 ; see paper for full list of authors ; The differential cross section for inclusive particle production as a function of energy in proton-proton collisions at a center-of-mass energy of 13 TeV is measured in the very forward region of the CMS detector. The measurement is based on data collected with the CMS apparatus at the LHC, and corresponds to an integrated luminosity of 0.35 inverse microbarns. The energy is measured in the CASTOR calorimeter, which covers the pseudorapidity region -6.6