  Using public \fermi LAT and \swift BAT observations, we constructed the first
sample of blazars selected at both hard X-rays and gamma-rays. Studying its
spectral properties, we find a luminosity dependence of the spectral slopes at
both energies. Specifically, luminous blazars, generally classified as FSRQs,
have {\it hard} continua in the medium-hard X-ray range but {\it soft} continua
in the LAT gamma-ray range (photon indices $\Gamma_X$ \ltsima 2 and $\Gamma_G$
\gtsima 2), while lower luminosity blazars, classified as BL Lacs, have
opposite 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 by
detailed Monte Carlo simulations explicitly taking into account the
observational biases of both instruments. Our results support the so-called
``blazar sequence'' which was originally based on radio samples of blazars and
radio luminosities. We also argue that the X-ray-to-gamma-ray continua of
blazars may provide independent insights into the physical conditions around
the jet, complementing/superseding the ambiguities of the traditional
classification based on optical properties.
