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apocalyptic n.  and  gapful n.

First numbers that belong to both sets:

192, 220, 286, 390, 583, 660, 671, 693, 700, 800, 1040, 1056, 1060, 1065, 1080, 1090, 1092, 1136, 1140, 1155, 1160, 1170, 1200, 1212, 1230, 1240, 1245, 1270, 1272, 1280, 1290, 1305, 1310, 1340, 1349, 1420, 1452, 1470, 1480, 1485, 1490, 1510, 1515, 1539, 1550, 1560, 1572, 1590, 1630, 1638, 1640, 1661, 1665, 1670, 1690, 1692, 1695, 1750, 1755, 1760, 1776, 1785, 1800, 1812, 1820, 1833, 1860, 1870, 1880, 1881, 1887, 1910, 1919, 1940, 1963, 1980, 1990, 1992, 2000, 2002, 2025, 2059, 2064, 2120, 2125, 2160, 2180, 2187, 2200, 2222, 2225, 2240, 2260, 2275, 2300, 2304, 2320, 2323, 2325, 2331, 2340, 2349, 2360, 2366, 2425, 2460, 2500, 2548, 2552, 2553, 2575, 2620, 2626, 2639, 2680, 2700, 2725, 2751, 2760, 2775, 2780, 2820, 2828, 2860, 2880, 2882, 2900, 2940, 2960, 2975, 2980, 2992, 3000, 3072, 3078, 3094, 3096, 3115, 3120, 3131, 3150, 3159, 3210, 3232, 3268, 3270, 3276, 3300, 3325, 3330, 3333, 3367, 3390, 3392, 3434, 3441, 3465, 3480, 3535, 3540, 3552, 3605, 3630, 3648, 3675, 3690, 3712, 3745, 3750, 3774, 3815, 3816, 3838, 3840, 3872, 3885, 3900, 3930, 3939, 3944, 3955, 3960, 3993, 3996, 4000, 4040, 4080, 4128, 4185, 4186, 4200, 4240, 4242, 4275, 4277, 4280, 4320, 4343, 4365, 4368, 4416, 4440, 4455, 4459, 4545, 4635, 4680, 4720, 4725, 4747, 4760, 4773, 4800, 4840, 4848, 4872, 4876, 4880, 4884, 4905, 4920, 4949, 4960, 4995, 5005, 5050, 5096, 5100, 5115, 5150, 5151, 5184, 5200, 5250, 5252, 5278, 5300, 5335, 5350, 5353, 5369, 5376, 5400, 5445, 5450, 5454, 5500, 5550, 5555, 5568, 5600, 5650, 5661, 5665, 5724, 5750, 5772, 5775, 5800, 5858, 5883, 5885, 5900, 5936, 5950, 6000, 6006, 6045, 6060, 6097, 6144, 6175, 6180, 6188, 6279, 6305, 6336, 6360, 6363, 6420.

Some larger examples :