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apocalyptic n.  and  pandigital

First numbers that belong to both sets:

714, 894, 898, 970, 1102, 1138, 1202, 1298, 1394, 1470, 1478, 1490, 1634, 1670, 1758, 1766, 1914, 1946, 2054, 2070, 2134, 2170, 2226, 2382, 2386, 2410, 2430, 2566, 2586, 2638, 2678, 2702, 2710, 2766, 2826, 2882, 2910, 2926, 2930, 8350, 8385, 8410, 8415, 8525, 8530, 8585, 8600, 8620, 8745, 8765, 8780, 8835, 8840, 8950, 8955, 8980, 8990, 9020, 10505, 10510, 10535, 10545, 10570, 10575, 11045, 11050, 11165, 11190, 11200, 11220, 11255, 11265, 11345, 11370, 11415, 11430, 11470, 11475, 11560, 11580, 11595, 11610, 11765, 11825, 11840, 11860, 11870, 12125, 12130, 12245, 12270, 12280, 12300, 12545, 12560, 12605, 12630, 12710, 12720, 12760, 12770, 12820, 12840, 12890, 12900, 13055, 13085, 13100, 13155, 13160, 13415, 13425, 13505, 13530, 13575, 13590, 13625, 13640, 13685, 13710, 13790, 13800, 14055, 14060, 14115, 14130, 14150, 14160, 14350, 14355, 14380, 14390, 14415, 14420, 14710, 14715, 14800, 14820, 14835, 14850, 14920, 14930, 14980, 15000, 15050, 15060, 15135, 15140, 15195, 15210, 15230, 15240, 15905, 15910, 15935, 15970, 15975, 16265, 16270, 16355, 16375, 16390, 16405, 16475, 16485, 16535, 16555, 16605, 16615, 16690, 16695, 16750, 16765, 16785, 16795, 16985, 16990, 17015, 17025, 17050, 17055, 17525, 17530, 17645, 17670, 17680, 17700, 17735, 17745, 17825, 17850, 17895, 17910, 17950, 17955, 18040, 18060, 18075, 18090, 19505, 19510, 19595, 19615, 19630, 19645, 19685, 19690, 19805, 19830, 19840, 19860, 20315, 20335, 20345, 20370, 20485, 20490, 20530, 20545, 20560, 20580, 20665, 20670, 20795, 20805, 20855, 20875, 20925, 20935, 20975, 20985, 21065, 21090, 21135, 21150, 21395, 21415, 21425, 21450, 21565, 21570, 21825, 21835, 21855, 21870, 21925, 21930, 22090, 22095, 22150, 22165, 22185, 22195, 22270, 22275, 22360, 22380, 22395, 22410, 22690, 22705, 22720, 22740, 22825, 22830, 22905, 22915, 22935, 22950, 23005, 23010, 23645, 23650, 23705, 23720, 23740, 23750, 23825, 23830, 23915.

Some larger examples :