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              <p>Context: Although it is commonly agreed that the presence of a close stellar companion is likely to affect planet formation and evolution, the precise effects and their actual impact on planet occurrence are still debated. Different conclusions have been reached on the theoretical side, while observational constraints are sparse, a consequence of the discrimination against close binaries in Doppler planet searches. Accordingly, basic questions such as how hospitable binaries are to planets and how binary separation and mass ratio impact on planet formation, remain poorly known. Aims: In an effort to bring observational constraints on the occurrence and properties of planets in binaries and multiple stars, we have been conducting a dedicated investigation, the results of which will be presented in this series. Methods: Our investigation follows two different approaches, one based on radial-velocity monitoring, the other based on direct imaging. In this first paper, we present the observational results from our systematic adaptive optics search with VLT/NACO for close stellar companions to 130 nearby stars, 57 with planets and 73 without, for comparison. The inclusion of a control sub-sample is a unique feature of our program that will enable a meaningful and rigorous comparison between the properties of planet-host stars and the properties of field stars subject to the same selection effects against close binaries, but showing no evidence for planetary companions. Results: Our data reveal 95 companion candidates found in the vicinity of 33 of our targets. Nineteen of these candidates are true companions and 2 are likely bound objects. Among planet-host stars, we discovered a tight pair of very low mass companions to HD 65216 (projected separation of 255 AU), an early M companion to HD 177830 (projected separation of 97 AU), and we resolved the previously known companion to HD 196050 into a close pair of M dwarfs. Our data additionally confirm the bound nature of the companions to HD 142, HD 16141, and HD 46375. Among control stars, we detected true companions to HD 7895, HD 24331, HD 31412, HD 40397, HD 43834, HD 70923, HD 78351, HD 104263, HD 129642, HD 154682, and HD 223913, and likely bound companions to HD 82241 and HD 134180. Most of these objects are M dwarfs and have projected separations between 7 and 505 AU. Based on observations collected at the ESO VLT Yepun telescope, proposals 70.C-0557, 71.C-0125, 73.C-0124, 74.C-0048, 75.C-0069, and 76.C-0057. Tables 1, 2, and Figs. 3, 4 are only available in electronic form at http://www.aanda.org</p>
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