Context. In past decades, huge surveys have confirmed the existence of populations of exotic and hitherto unknown quasar types. The discovery and investigation of these rare peculiar objects is important because they may represent links to special evolutionary stages and hold clues to the evolution of quasars and galaxies. Aims. The Sloan Digital Sky Survey (SDSS) discovered the unusual quasars J010540.75-003313.9 and J220445.27+003141.8 and a small number of similar objects. Their spectra are characterised by a break in the continuum around 3000 Å that neither shows the typical structure of broad absorption line (BAL) troughs nor is explained by typical intrinsic dust reddening. The main aim of the present paper was twofold. First, a new target-oriented search was performed in the spectra database of the SDSS to construct a sizable sample of such 3000 Å break quasars. Second, their broad-band spectral energy distribution (SED) was compared with SEDs of BAL quasars. Methods. We used the method of Kohonen self-organising maps for data mining in the SDSS spectra archive to search for more quasars with properties comparable to the prototypes J010540.75-003313.9 and J220445.27+003141.8. We constructed a sample of 3000 Å break quasars and comparison samples of quasars with similar properties, to some extent, but also showing indications for typical BAL features. Particular attention was payed to a possible contamination by rare stellar spectral types, in particular DQ white dwarfs. We construct ensemble-averaged broad-band SEDs based on archival data from SDSS, GALEX, 2MASS, UKIDSS, WISE, and other surveys. The SEDs were corrected for dust absorption at the systemic redshifts of the quasars by the comparison with the average SED of normal quasars. Results. We compiled a list of 23 quasars classified as 3000 Å break quasars with properties similar to 010540.75-003313.9 and J220445.27+003141.8. Their de-reddened arithmetic median composite SED is indistinguishable from that of the unusual BAL quasars. We conclude that 3000 Å break quasars are most likely extreme versions of BAL quasars. Assuming that the intrinsic SED of the continuum source is represented by the quasar composite SED, the 3000 Å break quasars tend to be intrinsically more luminous than ordinary quasars.