SIMBAD references

In this study, we analyze the ∼16 yr Fermi-Large Area Telescope data of 160 blazars consisting of 92 flat-spectrum radio quasars (FSRQs), 64 BL Lacertae (BL Lac)-type objects, and 4 blazar-candidates-of-unknown-type objects, and investigate their spectral variation. By fitting a linear model (y = kx + b) to the monthly binned flux-index plots, we find that most of the FSRQs (∼89%) display a harder-when-brighter trend (k > 0), while the majority of BL Lac-type objects (∼64%) exhibit a softer-when-brighter trend (k < 0). By plotting their slope (k) versus their variability index and inverse Compton (IC) peak frequency, we find a moderate positive correlation between k and the variability index and a moderate negative correlation between k and the IC peak frequency, which we name as the gamma-ray variability sequence of blazars. Additionally, eight blazars may not follow the linear variation trend, particularly in PKS 0537-441, AP Librae, and PKS 1510-089. Additional very-high-energy gamma-ray emission components may be the cause of the nonlinear variation trend.