37 new validated planets in overlapping K2 campaigns

We analysed 68 candidate planetary systems first identified during Campaigns 5 and 6 (C5 and C6) of the NASA \textit{K2} mission. We set out to validate these systems by using a suite of follow-up observations, including adaptive optics, speckle imaging, and reconnaissance spectroscopy. The overlap between C5 with C16 and C18, and C6 with C17, yields lightcurves with long baselines that allow us to measure the transit ephemeris very precisely, revisit single transit candidates identified in earlier campaigns, and search for additional transiting planets with longer periods not detectable in previous works. Using \texttt{vespa}, we compute false positive probabilities of less than 1\% for 37 candidates orbiting 29 unique host stars and hence statistically validate them as planets. These planets have a typical size of $2.2R_{\oplus}$ and orbital periods between 1.99 and 52.71 days. We highlight interesting systems including a sub-Neptune with the longest period detected by \textit{K2}, sub-Saturns around F stars, several multi-planetary systems in a variety of architectures. These results show that a wealth of planetary systems still remains in the \textit{K2} data, some of which can be validated using minimal follow-up observations and taking advantage of analyses presented in previous catalogs.