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lucky n.  and  repunit

First numbers that belong to both sets:

7, 13, 15, 21, 31, 43, 63, 73, 111, 127, 133, 211, 241, 259, 273, 307, 421, 463, 511, 553, 601, 651, 781, 931, 993, 1023, 1057, 1093, 1123, 1261, 1365, 1641, 1723, 1893, 2163, 2257, 2653, 2971, 3307, 3661, 4033, 4095, 4161, 5551, 5701, 6163, 6175, 7311, 7833, 8191, 8421, 8931, 9121, 9331, 9703, 9841, 10507, 10921, 11343, 11991, 14281, 14521, 15007, 16003, 16771, 18279, 18633, 20307, 21757, 22651, 22953, 23563, 24181, 25441, 26733, 27061, 28393, 29413, 29757, 30103, 31863, 33673, 36673, 38221, 39007, 39801, 40201, 40603, 42231, 42643, 43891, 44311, 47743, 47989, 49507, 51303, 52671, 53593, 54991, 57361, 57841, 58323, 60763, 61257, 65281, 65793, 66823, 67861, 71557, 74257, 75895, 75901, 80941, 81511, 83233, 90301, 92113, 95791, 96411, 98283, 99541, 101443, 102721, 103363, 104653, 111111, 115261, 115941, 116623, 120063, 122851, 124257, 124963, 125671, 127807, 128523, 130683, 131071, 138013, 138757, 139503, 141753, 142507, 144781, 150933, 155631, 161203, 162813, 168511, 172641, 180201, 188791, 194041, 200257, 202051, 204757, 208393, 215761, 219661, 224203, 227053, 228007, 230881, 231843, 238633, 247507, 248503, 250501, 251503, 253513, 255531, 258573, 260611, 265741, 266305, 266773, 271453, 278257, 282493, 284623, 287833, 293223, 296481, 298663, 301951, 304153, 308581, 316407, 317533, 318661, 319791, 325471, 327757, 335821, 335923, 338143, 339307, 345157, 347971, 351057, 352243, 357007, 364213, 367843, 370273, 372711, 376383, 378505, 388753, 391251, 398793, 402591, 407683, 410775, 424453, 427063, 437583, 438907, 446893, 448231, 450913, 452257, 463081, 464443, 468541, 474033, 476791, 478173, 480943, 483721, 494913, 507657, 510511, 511941, 524287, 526351, 530713, 532171, 536557, 539491, 542433, 552793, 555771, 561751, 566257, 575323, 590593, 593671, 595213, 597871, 606063, 607621, 612307, 613873, 618583, 620157, 626473, 631231, 632821, 636007, 637603, 644007, 663411, 665041, 669943, 673221, 674863, 678153, 679801, 688071, 689305, 699733, 704761, 709807, 711493, 719953, 737023, 742183, 749091, 757771.

Some larger examples :