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odious n.  and  repunit

First numbers that belong to both sets:

7, 13, 21, 31, 73, 91, 121, 127, 133, 157, 211, 241, 259, 273, 307, 341, 364, 381, 400, 421, 463, 511, 601, 651, 757, 781, 820, 871, 1057, 1123, 1261, 1407, 1483, 1555, 1561, 1807, 1893, 1981, 2047, 2071, 2257, 2353, 2380, 2551, 2653, 2801, 2955, 3193, 3280, 3423, 3661, 3907, 4033, 4161, 4291, 4557, 4681, 4831, 5113, 5220, 5257, 5403, 5461, 5551, 5853, 6163, 6175, 6643, 6973, 7141, 7240, 7483, 7657, 8011, 8191, 8557, 8931, 9313, 9331, 9703, 9724, 9841, 10101, 10921, 11111, 11557, 11773, 12433, 12657, 12883, 13111, 13341, 13807, 14281, 14425, 14763, 15253, 15751, 16276, 16513, 16771, 17293, 17823, 18279, 18361, 18907, 19461, 19531, 20023, 20307, 20440, 22053, 22651, 22765, 23257, 23563, 23871, 24493, 25260, 25441, 26083, 26407, 27061, 27931, 28057, 29071, 29413, 29757, 30451, 30784, 30801, 31153, 31507, 31863, 32767, 32943, 34783, 35157, 35911, 36673, 37057, 37060, 37831, 38613, 39007, 40201, 41007, 41413, 41821, 44136, 44311, 44733, 45157, 46011, 46441, 46873, 47307, 47989, 48181, 49507, 50401, 52060, 52213, 54241, 54523, 54991, 55933, 57361, 57841, 58807, 59293, 60763, 60880, 61753, 62751, 63757, 64771, 65281, 65641, 65793, 66307, 66430, 67341, 68383, 69433, 69905, 70491, 70644, 72093, 72631, 73713, 74257, 74803, 75351, 75895, 75901, 78121, 78681, 79243, 79807, 80373, 80941, 81400, 81511, 82657, 83811, 84391, 84973, 85557, 86731, 87381, 88507, 88741, 89103, 90301, 90903, 93196, 93331, 93943, 95791, 97033, 97656, 98911, 100173, 100807, 101443, 103363, 104007, 104653, 105951, 109231, 109893, 110557, 111223, 111891, 112561, 112945, 113233, 114583, 115261, 115941, 116623, 118681, 119371, 120063, 121453, 122151, 122851, 124257, 127807, 129241, 131071, 131407, 132133, 133591, 135793, 138013, 138757, 139503, 141753, 142507, 143365, 144781, 146307, 147841, 149383, 150933, 151711, 154057, 154843, 156421, 157213, 158803, 159601, 161203, 162007, 163621, 166057, 167691, 168421.

Some larger examples :