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gapful n.  and  happy n.

First numbers that belong to both sets:

100, 130, 176, 190, 192, 280, 440, 671, 700, 1000, 1030, 1090, 1092, 1125, 1152, 1185, 1188, 1212, 1215, 1221, 1274, 1275, 1290, 1300, 1330, 1332, 1335, 1390, 1484, 1512, 1547, 1572, 1575, 1670, 1717, 1725, 1752, 1755, 1760, 1771, 1785, 1812, 1815, 1818, 1875, 1880, 1881, 1900, 1920, 1930, 1992, 1995, 2080, 2093, 2112, 2121, 2175, 2260, 2275, 2300, 2331, 2360, 2425, 2457, 2475, 2548, 2575, 2620, 2639, 2725, 2751, 2784, 2800, 2825, 3367, 3392, 3456, 3465, 3535, 3605, 4004, 4040, 4275, 4365, 4400, 4455, 4545, 4635, 4640, 4725, 4747, 4872, 4960, 4995, 5187, 5335, 5353, 5445, 5454, 5555, 5650, 5724, 5994, 6305, 6435, 6528, 6825, 6955, 7000, 7125, 7171, 7425, 7474, 7488, 7630, 7840, 7878, 8099, 8181, 8245, 8256, 8787, 8880, 9785, 9975, 10000, 10030, 10090, 10092, 10125, 10152, 10185, 10188, 10212, 10215, 10275, 10290, 10300, 10330, 10332, 10335, 10390, 10444, 10512, 10557, 10572, 10575, 10670, 10724, 10725, 10727, 10752, 10755, 10760, 10785, 10812, 10815, 10818, 10875, 10880, 10900, 10920, 10930, 10933, 10976, 10992, 10995, 11025, 11052, 11085, 11088, 11120, 11140, 11145, 11150, 11205, 11210, 11214, 11220, 11229, 11232, 11250, 11280, 11284, 11292, 11341, 11358, 11385, 11410, 11412, 11415, 11419, 11451, 11456, 11480, 11510, 11520, 11538, 11564, 11580, 11583, 11595, 11770, 11805, 11808, 11820, 11832, 11835, 11840, 11843, 11850, 11880, 11914, 11917, 11955, 12012, 12015, 12075, 12090, 12105, 12110, 12120, 12132, 12150, 12176, 12180, 12192, 12194, 12210, 12220, 12256, 12312, 12330, 12348, 12438, 12465, 12470, 12474, 12510, 12570, 12580, 12645, 12672, 12705, 12740, 12750, 12767, 12770, 12792, 12810, 12850, 12880, 12900, 12912, 12939, 12972, 12990, 13000, 13030, 13032, 13035, 13090, 13158, 13185, 13212, 13230, 13248, 13300, 13305, 13320, 13330, 13332, 13350, 13370, 13390, 13428, 13447, 13518, 13530, 13575.

Some larger examples :