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Duffinian n.  and  plaindrome

First numbers that belong to both sets:

4, 8, 9, 16, 25, 27, 35, 36, 39, 49, 55, 57, 77, 111, 115, 119, 125, 128, 129, 133, 144, 155, 169, 189, 225, 235, 237, 245, 247, 256, 259, 279, 289, 299, 333, 335, 338, 355, 377, 399, 469, 489, 559, 567, 578, 579, 589, 667, 669, 689, 777, 779, 799, 889, 899, 999, 1111, 1115, 1119, 1127, 1133, 1135, 1137, 1147, 1156, 1157, 1159, 1177, 1189, 1225, 1227, 1247, 1255, 1299, 1333, 1337, 1349, 1355, 1357, 1359, 1369, 1379, 1389, 1444, 1445, 1457, 1467, 1469, 1477, 1555, 1569, 1577, 1589, 1677, 1679, 1799, 1899, 2227, 2233, 2249, 2255, 2257, 2279, 2289, 2335, 2345, 2359, 2369, 2379, 2449, 2455, 2469, 2479, 2489, 2555, 2559, 2567, 2569, 2577, 2599, 2667, 2669, 2779, 2888, 2899, 3337, 3349, 3355, 3357, 3369, 3379, 3445, 3455, 3459, 3477, 3479, 3569, 3577, 3589, 3599, 3667, 3679, 3689, 3789, 3799, 3899, 3999, 4445, 4449, 4467, 4469, 4477, 4489, 4499, 4555, 4559, 4577, 4579, 4589, 4599, 4667, 4669, 4699, 4777, 5555, 5567, 5599, 5679, 5699, 5777, 5789, 5799, 5889, 5899, 5999, 6667, 6669, 6677, 6789, 6799, 6889, 7777, 7779, 7799, 7889, 7999, 8899, 11111, 11123, 11127, 11129, 11133, 11135, 11137, 11147, 11155, 11167, 11179, 11189, 11199, 11227, 11233, 11236, 11237, 11245, 11249, 11255, 11259, 11267, 11269, 11333, 11335, 11339, 11347, 11357, 11359, 11367, 11377, 11379, 11389, 11449, 11457, 11469, 11477, 11555, 11559, 11567, 11569, 11599, 11667, 11669, 11889, 11899, 11999, 12223, 12225, 12229, 12233, 12235, 12247, 12257, 12259, 12279, 12333, 12335, 12337, 12339, 12349, 12355, 12359, 12367, 12369, 12389, 12449, 12455, 12459, 12469, 12477, 12499, 12557, 12559, 12599, 12667, 12677, 12679, 12779, 12999, 13333, 13345, 13347, 13349, 13355, 13359, 13369, 13379, 13447, 13448, 13449, 13456, 13459.

Some larger examples :