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iban n.  and  palindromic n.

First numbers that belong to both sets:

1, 2, 3, 4, 7, 11, 22, 44, 77, 101, 111, 121, 141, 171, 202, 212, 222, 242, 272, 303, 323, 343, 373, 404, 414, 424, 444, 474, 707, 717, 727, 747, 777, 1001, 1111, 1221, 1441, 1771, 2002, 2112, 2222, 2442, 2772, 3003, 3223, 3443, 3773, 4004, 4114, 4224, 4444, 4774, 7007, 7117, 7227, 7447, 7777, 10001, 10101, 10201, 10301, 10401, 10701, 11011, 11111, 11211, 11311, 11411, 11711, 12021, 12121, 12221, 12321, 12421, 12721, 14041, 14141, 14241, 14341, 14441, 14741, 17071, 17171, 17271, 17371, 17471, 17771, 20002, 20102, 20202, 20302, 20402, 20702, 21012, 21112, 21212, 21312, 21412, 21712, 22022, 22122, 22222, 22322, 22422, 22722, 24042, 24142, 24242, 24342, 24442, 24742, 27072, 27172, 27272, 27372, 27472, 27772, 40004, 40104, 40204, 40304, 40404, 40704, 41014, 41114, 41214, 41314, 41414, 41714, 42024, 42124, 42224, 42324, 42424, 42724, 44044, 44144, 44244, 44344, 44444, 44744, 47074, 47174, 47274, 47374, 47474, 47774, 70007, 70107, 70207, 70307, 70407, 70707, 71017, 71117, 71217, 71317, 71417, 71717, 72027, 72127, 72227, 72327, 72427, 72727, 74047, 74147, 74247, 74347, 74447, 74747, 77077, 77177, 77277, 77377, 77477, 77777, 100001, 101101, 102201, 103301, 104401, 107701, 110011, 111111, 112211, 114411, 117711, 120021, 121121, 122221, 123321, 124421, 127721, 140041, 141141, 142241, 143341, 144441, 147741, 170071, 171171, 172271, 173371, 174471, 177771, 200002, 201102, 202202, 203302, 204402, 207702, 210012, 211112, 212212, 214412, 217712, 220022, 221122, 222222, 223322, 224422, 227722, 240042, 241142, 242242, 243342, 244442, 247742, 270072, 271172, 272272, 273372, 274472, 277772, 300003, 301103, 302203, 303303, 304403, 307703, 320023, 321123, 322223, 323323, 324423, 327723, 340043, 341143, 342243, 343343, 344443, 347743, 370073, 371173, 372273, 373373, 374473, 377773, 400004, 401104, 402204, 403304, 404404, 407704, 410014, 411114, 412214, 414414, 417714, 420024, 421124, 422224, 423324, 424424, 427724, 440044, 441144, 442244, 443344.

Some larger examples :