Recurring outbursts of the supernova impostor AT 2016blu in NGC 4559

We present the first photometric analysis of the supernova (SN) impostor AT 2016blu in NGC 4559. This transient was discovered by the Lick Observatory Supernova Search in 2012 and has continued its outbursts since then. Optical and infrared photometry of AT 2016blu reveals at least 19 outbursts in 2012-2022. Similar photometry from 1999-2009 shows no outbursts, indicating that the star was relatively stable in the decade before discovery. Archival {\it Hubble Space Telescope} observations suggest that the progenitor had a minimum initial mass of $M >= 33$ M$_{\odot}$ and a luminosity of $L >= 10^{5.7}$ L$_{\odot}$. AT 2016blu's outbursts show irregular variability with multiple closely spaced peaks having typical amplitudes of 1-2 mag and durations of 1-4 weeks. While individual outbursts have irregular light curves, concentrations of these peaks recur with a period of $\sim 113 \pm 2$ d. Based on this period, we predict times for upcoming outbursts in 2023 and 2024. AT 2016blu shares similarities with SN 2000ch in NGC 3432, where outbursts may arise from periastron encounters in an eccentric binary containing a luminous blue variable (LBV). We propose that AT 2016blu's outbursts are also driven by interactions that intensify around periastron in an eccentric system. Intrinsic variability of the LBV-like primary star may cause different intensity and duration of binary interaction at each periastron passage. AT 2016blu also resembles the periastron encounters of $η$ Carinae prior to its Great Eruption and the erratic pre-SN eruptions of SN 2009ip. This similarity and the onset of eruptions in the past decade hint that AT 2016blu may also be headed for a catastrophe, making it a target of great interest.