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Artificial intelligence based on artificial neural networks, which are originally inspired by the biological architectures of the human brain, has mostly been realized using software but executed on conventional von Neumann computers, where the so-called von Neumann bottleneck essentially limits the executive efficiency due to the separate computing and storage units. Therefore, a suitable hardware platform that can exploit all the advantages of brain-inspired computing is highly desirable. Based upon micromagnetic simulation of the magnetization dynamics, we demonstrate theoretically and numerically that recurrent neural networks consisting of as few as 40 magnetic tunnel junctions can generate and recognize periodic time series after they are trained with an efficient algorithm.