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We calculate the equation of state at high temperatures in 2+1 flavor QCD using the highly improved staggered quark (HISQ) action. We study the lattice spacing dependence of the pressure at high temperatures using lattices with temporal extent Nτ=6, 8, 10 and 12 and perform continuum extrapolations. We also give a continuum estimate for the equation of state up to temperatures T=2 GeV, which are then compared with results of the weak-coupling calculations. We find a reasonably good agreement with the weak-coupling calculations at the highest temperatures.