INTEGRAL observed the nova V5668 Sgr around the time of its optical maximum on March 21, 2015. Studies at UV wavelengths showed spectral lines of freshly produced Be-7. This could be measurable also in gamma-rays at 478 keV from the decay to Li-7. Novae are also expected to synthesise Na-22 which decays to Ne-22, emitting a 1275 keV photon. About one week before the optical maximum, a strong gamma-ray flash on time-scales of hours is expected from short-lived radioactive nuclei, such as N-13 and F-18. These beta-plus-unstable nuclei should yield emission up to 511 keV, but which has never been observed. The spectrometer SPI aboard INTEGRAL pointed towards V5668 by chance. We use these observations to search for possible gamma-ray emission of decaying Be-7, and to directly measure the synthesised mass during explosive burning. We also aim to constrain possible burst-like emission days to weeks before the optical maximum using the SPI anticoincidence shield (ACS). We extract spectral and temporal information to determine the fluxes of gamma-ray lines at 478 keV, 511 keV, and 1275 keV. A measured flux value directly converts into abundances produced by the nova. The SPI-ACS rates are analysed for burst-like emission using a nova model light-curve. For the obtained nova flash candidate events, we discuss possible origins. No significant excess for the expected gamma-ray lines is found. Our upper limits on the synthesised Be-7 and Na-22 mass depend on the uncertainties of the distance to the nova: The Be-7 mass is constrained to less than $4.8times10^{-9},(d/kpc)^2$, and Na-22 to less than $2.4times10^{-8},(d/kpc)^2$ solar masses. For the Be-7 mass estimate from UV studies, the distance to V5668 Sgr must be larger than 1.2 kpc. During three weeks before the optical maximum, we find 23 burst-like events in the ACS rate, of which six could possibly be associated with V5668 Sgr.
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