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evil n.  and  repunit

First numbers that belong to both sets:

15, 40, 43, 57, 63, 85, 111, 156, 183, 255, 343, 507, 553, 585, 703, 813, 931, 993, 1023, 1093, 1111, 1191, 1333, 1365, 1464, 1641, 1723, 1885, 2163, 2451, 2757, 2863, 2971, 3081, 3307, 3541, 3616, 3783, 3906, 4095, 4369, 4423, 4693, 4971, 5701, 6007, 6321, 6481, 6807, 7311, 7381, 7833, 8373, 8421, 8743, 9121, 9507, 9901, 10303, 10507, 10713, 11131, 11155, 11343, 11991, 12211, 12720, 13573, 14043, 14521, 15007, 15501, 16003, 16105, 16257, 16383, 17031, 17557, 18091, 18633, 19183, 19608, 19741, 20593, 20881, 21171, 21463, 21757, 21845, 22351, 22621, 22953, 24181, 24807, 25123, 25761, 26733, 27391, 27723, 28393, 28731, 29524, 30103, 30941, 32221, 32581, 33307, 33673, 33825, 34041, 34411, 35533, 36291, 37443, 37449, 38221, 39403, 39801, 40495, 40603, 41371, 42231, 42643, 43057, 43473, 43891, 45583, 47743, 48621, 49063, 49953, 50851, 51303, 51757, 52671, 53131, 53593, 54057, 55461, 55987, 56355, 56407, 56883, 58323, 59781, 60271, 61257, 62251, 63253, 64263, 65535, 66823, 67861, 68907, 69961, 71023, 71557, 73171, 76453, 77007, 77563, 82083, 83233, 86143, 87165, 87321, 87913, 88573, 89701, 91507, 92113, 92721, 94557, 95173, 96411, 97657, 98283, 99499, 99541, 102081, 102721, 105301, 106080, 106603, 107257, 107913, 108571, 111111, 111151, 113907, 117307, 117993, 120100, 120757, 123553, 124963, 125671, 126381, 127093, 127551, 128523, 129961, 130683, 132861, 134323, 135057, 135304, 136531, 137257, 137271, 137561, 140251, 141001, 143263, 144021, 145543, 147073, 148611, 150157, 151740, 152491, 153273, 155631, 158007, 160401, 160435, 162813, 164431, 165243, 166873, 168511, 169333, 170983, 171811, 173473, 175981, 176821, 177156, 177663, 178507, 179353, 181051, 181903, 182757, 185331, 186193, 187057, 187923, 190533, 192283, 194923, 195807, 196693, 199363, 202051, 204757, 207481, 208393, 208920, 209307, 218557, 219493, 221371, 223257, 224203, 228007, 228963, 229921, 235711, 236683, 237657, 238633, 239611, 241573, 244531, 245411, 246513, 248503, 249501, 252507.

Some larger examples :