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iban n.  and  modest n.

First numbers that belong to both sets:

23, 103, 111, 203, 211, 222, 311, 327, 411, 412, 422, 444, 711, 721, 777, 1003, 1011, 1022, 1027, 1111, 1222, 1227, 1244, 1421, 1422, 1442, 1477, 2003, 2022, 2027, 2044, 2074, 2111, 2127, 2177, 2222, 2427, 2444, 2472, 3027, 3111, 3244, 3272, 4012, 4027, 4044, 4072, 4074, 4111, 4222, 4277, 4444, 7021, 7027, 7077, 7111, 7777, 10003, 10011, 10027, 10074, 10101, 10111, 10222, 10270, 10303, 10370, 11027, 11111, 11407, 12027, 12074, 12111, 12222, 12324, 12444, 14021, 14027, 14042, 14074, 14111, 14222, 14777, 17027, 17111, 20003, 20011, 20022, 20027, 20074, 20101, 20111, 20202, 20222, 20270, 20303, 20370, 20444, 20740, 21027, 21111, 21777, 22027, 22074, 22111, 22222, 22407, 23027, 23111, 23207, 24027, 24072, 24074, 24111, 24222, 24324, 24444, 27111, 27243, 40011, 40012, 40022, 40044, 40072, 40074, 40101, 40111, 40120, 40202, 40222, 40270, 40303, 40370, 40404, 40444, 40740, 41111, 41123, 41212, 42074, 42111, 42222, 42777, 43111, 44074, 44111, 44222, 44407, 44444, 47111, 47141, 47423, 70011, 70021, 70074, 70077, 70101, 70111, 70210, 70222, 70270, 70303, 70370, 70707, 70777, 71111, 72074, 72111, 72121, 72222, 72243, 72324, 72444, 73111, 74111, 74222, 77111, 77407, 77777, 100003, 100011, 100022, 100041, 100101, 100110, 100111, 100123, 100202, 100222, 100270, 100271, 100300, 100303, 100370, 100444, 100740, 101010, 101111, 101303, 102111, 102222, 103111, 104111, 104117, 104222, 104312, 104444, 104702, 107111, 107321, 110101, 110111, 110121, 110222, 110270, 110303, 110370, 110407, 111111, 112144, 112222, 112444, 112777, 114171, 114222, 114342, 114703, 117243, 120022, 120027, 120044, 120101, 120202, 120222, 120270, 120303, 120324, 120370, 120404, 120444, 120740, 121111, 121212, 121407, 122222, 122727, 124222, 124372, 124444, 140021, 140022, 140042, 140077, 140101, 140202, 140210, 140222, 140270, 140303, 140370, 140420, 140444, 140707, 140740, 140777, 141111, 141414, 141423, 142121, 142222, 143407, 144222, 144242, 144243, 144324, 144444, 147441, 147777, 170101, 170222.

Some larger examples :