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Using public \fermi LAT and \swift BAT observations, we constructed the firstsample of blazars selected at both hard X-rays and gamma-rays. Studying itsspectral properties, we find a luminosity dependence of the spectral slopes atboth energies. Specifically, luminous blazars, generally classified as FSRQs,have {\it hard} continua in the medium-hard X-ray range but {\it soft} continuain the LAT gamma-ray range (photon indices $\Gamma_X$ \ltsima 2 and $\Gamma_G$\gtsima 2), while lower luminosity blazars, classified as BL Lacs, haveopposite behavior, i.e., {\it soft} X-ray and {\it hard} gamma-ray continua($\Gamma_X$ \gtsima 2.4 and $\Gamma_G < 2$). The trends are confirmed bydetailed Monte Carlo simulations explicitly taking into account theobservational biases of both instruments. Our results support the so-called``blazar sequence'' which was originally based on radio samples of blazars andradio luminosities. We also argue that the X-ray-to-gamma-ray continua ofblazars may provide independent insights into the physical conditions aroundthe jet, complementing/superseding the ambiguities of the traditionalclassification based on optical properties.

Swift BAT, Fermi LAT, and the Blazar Sequence