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aban n.  and  cyclic n.

First numbers that belong to both sets:

1, 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 33, 35, 37, 41, 43, 47, 51, 53, 59, 61, 65, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 91, 95, 97, 101, 103, 107, 109, 113, 115, 119, 123, 127, 131, 133, 137, 139, 141, 143, 145, 149, 151, 157, 159, 161, 163, 167, 173, 177, 179, 181, 185, 187, 191, 193, 197, 199, 209, 211, 213, 215, 217, 221, 223, 227, 229, 233, 235, 239, 241, 247, 249, 251, 255, 257, 259, 263, 265, 267, 269, 271, 277, 281, 283, 287, 293, 295, 299, 303, 307, 311, 313, 317, 319, 321, 323, 329, 331, 335, 337, 339, 341, 345, 347, 349, 353, 359, 365, 367, 371, 373, 377, 379, 383, 389, 391, 393, 395, 397, 401, 403, 407, 409, 411, 413, 415, 419, 421, 427, 431, 433, 435, 437, 439, 443, 445, 447, 449, 451, 455, 457, 461, 463, 467, 469, 473, 479, 481, 485, 487, 491, 493, 499, 501, 503, 509, 511, 515, 517, 519, 521, 523, 527, 533, 535, 537, 541, 545, 547, 551, 553, 557, 559, 561, 563, 565, 569, 571, 573, 577, 581, 583, 587, 589, 591, 593, 595, 599, 601, 607, 611, 613, 617, 619, 623, 629, 631, 635, 641, 643, 647, 649, 653, 659, 661, 665, 667, 671, 673, 677, 679, 681, 683, 685, 691, 695, 697, 699, 701, 703, 705, 707, 709, 713, 717, 719, 721, 727, 731, 733, 739, 743, 745, 749, 751, 753, 757, 761, 763, 767, 769, 771, 773, 779, 781, 785, 787, 789, 793, 795, 797, 799, 803, 805, 807, 809, 811, 815, 817, 821, 823, 827, 829, 835, 839, 843, 851.

Some larger examples :