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gapful n.  and  nude n.

First numbers that belong to both sets:

132, 135, 264, 315, 396, 1111, 1155, 1212, 1296, 1332, 1335, 1344, 1368, 1395, 1515, 1575, 1632, 1692, 1764, 1771, 1935, 2112, 2128, 2184, 2222, 2424, 2664, 2688, 2772, 3264, 3276, 3333, 3636, 3648, 3816, 3996, 4128, 4224, 4368, 4416, 4444, 4848, 4872, 5115, 5555, 5775, 6144, 6336, 6666, 7777, 8448, 8888, 9216, 9999, 11112, 11115, 11136, 11144, 11172, 11232, 11355, 11412, 11424, 11448, 11535, 11616, 11832, 12124, 12132, 12168, 12264, 12312, 12336, 12432, 12492, 12612, 12816, 12824, 12888, 13155, 13212, 13248, 13272, 13332, 13335, 13392, 13515, 13632, 13755, 13776, 13932, 13968, 13995, 14112, 14224, 14232, 14292, 14328, 14364, 14412, 14688, 14784, 14832, 15135, 15315, 15555, 16128, 16212, 16332, 16416, 16464, 16488, 16632, 16848, 16992, 17115, 17136, 17171, 17444, 17472, 17535, 17724, 17955, 18144, 18288, 18312, 18336, 18424, 18432, 18648, 18816, 19296, 19332, 19368, 19395, 19692, 19935, 21144, 21168, 21216, 21264, 21384, 21448, 21624, 21728, 21864, 21996, 22224, 22288, 22344, 22464, 22824, 22848, 23166, 23184, 23232, 23424, 23664, 23688, 24112, 24144, 24248, 24264, 24336, 24384, 24624, 24864, 24984, 26184, 26424, 26664, 27384, 27412, 27888, 28224, 28344, 28448, 28464, 28728, 28824, 28944, 29664, 31392, 31824, 31896, 32436, 32616, 32832, 33288, 33312, 33336, 33696, 33864, 34236, 34272, 34416, 34776, 35175, 35595, 36216, 36396, 36936, 37296, 37632, 38112, 39375, 39636, 39816, 39996, 41184, 41328, 41412, 41832, 42288, 42672, 43164, 43248, 43488, 43824, 44436, 44448, 44688, 44772, 44928, 46128, 46368, 46464, 46848, 46872, 47124, 47712, 48224, 48288, 49248, 49392, 49968, 51315, 51975, 53955, 55935, 61116, 61824, 62436, 63612, 63648, 64416, 66624, 68376, 69192, 69696, 73416, 77112, 77175, 79632, 81144, 81488, 82368, 82824, 83664, 83688, 84128, 86184, 86328, 87864, 91296, 91728, 92736, 93195, 94392, 96444, 98496, 99936, 111111, 111132, 111135, 111168, 111195, 111216, 111244, 111312.

Some larger examples :