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gapful n.  and  self n.

First numbers that belong to both sets:

108, 110, 121, 132, 143, 154, 165, 176, 187, 198, 400, 1032, 1065, 1098, 1111, 1155, 1188, 1210, 1212, 1245, 1278, 1300, 1313, 1335, 1368, 1390, 1414, 1425, 1458, 1480, 1515, 1548, 1570, 1616, 1638, 1660, 1717, 1728, 1750, 1818, 1840, 1919, 1930, 1963, 1974, 2112, 2200, 2268, 2325, 2380, 2560, 2639, 2740, 2751, 2784, 2920, 2975, 2997, 3045, 3078, 3392, 3605, 3774, 4360, 4551, 4720, 4876, 4920, 5115, 5350, 6000, 6305, 6720, 6900, 7104, 7420, 7980, 8320, 8880, 10032, 10065, 10098, 10155, 10188, 10210, 10212, 10234, 10245, 10256, 10278, 10300, 10335, 10368, 10390, 10425, 10458, 10469, 10480, 10515, 10548, 10570, 10638, 10660, 10728, 10750, 10794, 10816, 10818, 10840, 10930, 11055, 11088, 11110, 11112, 11145, 11178, 11200, 11235, 11268, 11290, 11325, 11358, 11380, 11415, 11448, 11470, 11538, 11560, 11628, 11650, 11718, 11740, 11830, 11920, 12045, 12078, 12100, 12111, 12124, 12135, 12168, 12179, 12190, 12225, 12258, 12280, 12315, 12348, 12370, 12416, 12427, 12438, 12460, 12493, 12528, 12550, 12618, 12640, 12684, 12730, 12820, 12976, 13035, 13068, 13090, 13101, 13125, 13136, 13158, 13180, 13215, 13248, 13270, 13314, 13338, 13360, 13428, 13450, 13518, 13540, 13617, 13630, 13663, 13696, 13720, 13920, 13944, 14010, 14025, 14058, 14080, 14091, 14115, 14148, 14170, 14238, 14260, 14328, 14350, 14416, 14418, 14440, 14530, 14574, 14620, 14820, 14833, 14910, 15000, 15048, 15070, 15081, 15138, 15160, 15204, 15228, 15250, 15318, 15340, 15430, 15520, 15720, 15810, 15834, 15856, 15900, 15979, 15990, 16038, 16060, 16071, 16128, 16150, 16218, 16240, 16330, 16420, 16464, 16576, 16620, 16677, 16710, 16800, 16890, 16980, 17028, 17050, 17061, 17094, 17118, 17140, 17173, 17230, 17296, 17320, 17520, 17610, 17689, 17700, 17724, 17790, 17823, 17880, 17970, 18040, 18051, 18130, 18207, 18220, 18343, 18354, 18420, 18510, 18600, 18690, 18736, 18780, 18870, 18914, 18960.

Some larger examples :