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Trigonometric parallaxes measured with ground-based telescopes of the RECONS consortium as part of the CTIOPI program are used to search for stars that have either had an encounter with the solar system in the past or will have such an encounter in the future, at distances of less than a few parsecs. These are mainly low-mass dwarfs and subdwarfs of types M, L, and T currently at distances of less than 30 pc from the Sun. Six stars for which encounters with the solar orbit at distances of less than 1 pc are possible have been identified for the first time. For example, the minimum distance for the star **SOZ 3A will 0.72+/- 0.11 pc at an epoch of 103+/-44 thousand years in the future.

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