By recording multiple cells simultaneously, electrophysiologists have found evidence for repeating spatiotemporal spike patterns, which can carry information. How this information is extracted by downstream neurons is unclear. In this theoretical paper, we investigate to what extent a single cell could detect a given spike pattern and what the optimal parameters to do so are, in particular the membrane time constant $τ$. Using a leaky integrate-and-fire (LIF) neuron with instantaneous synapses and homogeneous Poisson input, we were able to compute this optimum analytically. Our results indicate that a relatively small $τ$ (at most a few tens of ms) is usually optimal, even when the pattern is much longer. This is somewhat counter intuitive as the resulting detector ignores most of the pattern, due to its fast memory decay. Next, we wondered if spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimum. We simulated a LIF neuron equipped with additive spike-timing-dependent potentiation and homeostatic rate-based depression, and repeatedly exposed it to a given input spike pattern. As in previous studies, the LIF progressively became selective to the repeating pattern with no supervision, even when the pattern was embedded in Poisson activity. Here we show that, using certain STDP parameters, the resulting pattern detector can be optimal. Taken together, these results may explain how humans can learn repeating visual or auditory sequences. Long sequences could be recognized thanks to coincidence detectors working at a much shorter timescale. This is consistent with the fact that recognition is still possible if a sound sequence is compressed, played backward, or scrambled using 10ms bins. Coincidence detection is a simple yet powerful mechanism, which could be the main function of neurons in the brain.