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balanced n.  and  nude n.

First numbers that belong to both sets:

2, 9, 11, 12, 15, 44, 99, 135, 184, 212, 216, 312, 384, 396, 412, 424, 555, 612, 624, 666, 728, 824, 936, 2166, 2222, 2226, 2262, 2364, 2412, 2424, 2488, 2744, 2772, 2916, 3111, 3126, 3132, 3162, 3171, 3222, 3276, 3288, 3312, 3339, 3366, 3384, 3432, 3492, 3612, 3636, 3666, 3717, 3864, 3888, 7175, 9126, 9144, 9162, 9333, 11111, 11112, 11155, 11172, 11184, 11232, 11322, 11331, 11355, 11436, 11444, 11448, 11535, 11555, 11688, 11711, 11832, 11888, 11916, 12112, 12128, 12162, 12168, 12224, 12412, 12636, 13155, 13224, 13335, 13515, 13644, 13713, 13755, 13776, 14128, 14212, 14224, 14444, 15135, 15575, 17115, 17199, 17262, 17955, 18168, 18936, 19944, 21432, 22764, 23244, 23436, 24264, 24288, 26316, 26412, 26424, 27762, 28128, 28368, 28488, 29412, 31116, 31344, 31515, 31632, 31848, 31896, 32136, 32262, 32292, 32322, 32328, 33135, 33399, 33555, 34236, 34776, 35175, 35955, 36126, 36216, 36312, 36324, 36336, 36444, 36636, 36816, 37737, 38136, 38328, 38616, 38832, 39132, 39195, 39222, 39366, 39375, 39384, 39393, 39636, 39888, 39996, 41212, 41436, 41848, 42412, 42424, 42444, 42612, 42728, 42864, 44124, 44212, 44244, 44248, 44316, 44364, 44436, 44488, 44496, 44744, 44824, 44848, 46236, 46296, 46488, 46644, 46692, 46872, 46944, 47824, 48184, 48216, 48336, 48424, 48432, 49644, 51315, 51555, 51975, 53355, 53955, 55335, 55395, 61248, 61644, 61848, 62226, 62232, 62244, 62616, 62664, 62688, 63168, 63264, 63636, 63816, 63888, 63936, 64644, 131193, 131775, 131931, 133311, 133371, 133626, 134124, 134136, 136122, 136662, 136692, 137172, 138168, 138216, 139995, 141212, 141288, 141816, 142236, 142772, 142824, 143244, 143328, 144244, 144248, 144312, 144732, 144824, 144872, 146124, 146136, 146232, 146316, 146328, 146616, 146664, 147112, 147168, 147224, 147336, 149364, 151115, 153555, 155155, 161112, 161124, 161136, 161232, 161322, 161364, 161448, 161616, 161964, 162132, 162216, 162444, 163362, 163368, 163464, 163488, 166266.

Some larger examples :