Quasars with extremely red infrared-to-optical colours are an interesting population that can test ideas about quasar evolution as well as orientation, obscuration and geometric effects in the so-called AGN unified model. To identify such a population we match the quasar catalogues of the Sloan Digital Sky Survey (SDSS), the Baryon Oscillation Spectroscopic Survey (BOSS) to the Wide-Field Infrared Survey Explorer (WISE) to identify quasars with extremely high infrared-to-optical ratios. We identify 65 objects with r(AB)-W4(Vega)>14 mag (i.e., F_nu(22um)/F_nu(r) > ~1000). This sample spans a redshift range of 0.28<z<4.36 and has a bimodal distribution, with peaks at z~0.8 and z~2.5. It includes three z>2.6 objects that are detected in the W4-band but not W1 or W2 (i.e., W1W2-dropouts). The SDSS/BOSS spectra show that the majority of the objects are reddened Type 1 quasars, Type 2 quasars (both at low and high redshift) or objects with deep low-ionization broad absorption lines (BALs) that suppress the observed r-band flux. In addition, we identify a class of Type 1 permitted broad-emission line objects at z~2-3 which are characterized by emission line rest-frame equivalent widths (REWs) of >~150Ang , much larger than those of typical quasars. In particular, 55% (45%) of the non-BAL Type 1s with measurable CIV in our sample have REW(CIV) > 100 (150)Ang, compared to only 5.8% (1.3%) for non-BAL quasars in BOSS. These objects often also have unusual line ratios, such as very high NV/Ly-alpha ratios. These large REWs might be caused by suppressed continuum emission analogous to Type 2 quasars; however, there is no obvious mechanism in standard Unified Models to suppress the continuum without also obscuring the broad emission lines.
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