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balanced n.  and  vampire n.

First numbers that belong to both sets:

136948, 145314, 152685, 175329, 201852, 213466, 215860, 226498, 226872, 254740, 286416, 362992, 457600, 629680, 679500, 769792, 794088, 841995, 939658, 10042510, 10102252, 10128235, 10129900, 10134985, 10165680, 10192248, 10195794, 10217493, 10233054, 10237864, 10250460, 10254100, 10255000, 10293966, 10294200, 10437678, 10461784, 10502100, 10522350, 10671417, 10742868, 10792390, 10821600, 10832850, 10835370, 10851939, 10935436, 11064280, 11074657, 11085304, 11158735, 11185762, 11246800, 11286193, 11306857, 11330865, 11438266, 11506770, 11557323, 11564280, 11677140, 11727625, 11753874, 11766892, 11803482, 11844832, 11850394, 11867467, 11883613, 11887524, 11920468, 11920657, 11925540, 11929918, 11970256, 11982348, 12006000, 12060027, 12097350, 12098646, 12128935, 12145693, 12159720, 12195760, 12210588, 12247686, 12274515, 12276400, 12371904, 12383059, 12384000, 12408385, 12448800, 12485115, 12620790, 12645360, 12684924, 12698334, 12735895, 12754075, 12832524, 12873294, 12885147, 13024480, 13041909, 13062460, 13208670, 13230945, 13234864, 13241974, 13268772, 13427500, 13494793, 13542880, 13545000, 13754790, 13777816, 13794480, 13918621, 14035126, 14186790, 14279832, 14340690, 14350360, 14365260, 14452879, 14553270, 14618695, 14642208, 14652000, 14653728, 14728648, 14736780, 14739340, 14799555, 14936400, 14974596, 15026008, 15063264, 15088324, 15169576, 15227100, 15249780, 15262870, 15266272, 15293250, 15337287, 15372630, 15450228, 15502662, 15623460, 15625984, 15742350, 15842344, 15862063, 15931201, 16142620, 16276320, 16335450, 16398144, 16425364, 16534804, 16598344, 33674971, 33905650, 34317918, 34437964, 34514662, 34536226, 34696318, 34789180, 35018973, 35289315, 35542678, 35608936, 35609476, 35841897, 35909775, 36420448, 36529438, 36781420, 36788431, 36820840, 36948870, 37045435, 37066410, 37598017, 37699200, 38164450, 38196945, 38735284, 38894278, 38985664, 39040177, 39167892, 39204126, 39413542, 39644212, 39724825, 40549968, 40556776, 40749268, 40774369, 40885312, 41259190, 41309842, 41449009, 41507986, 41559367, 41592496, 41747580, 42036939, 42573397, 42591604, 42595780, 42974352, 43461972, 43687512, 43862260, 44577598, 45065475, 45185872, 45193383, 45319950, 45373126, 45476064, 45606528, 45819180, 45896305, 45917028, 45962824, 46017670, 46019520, 46327918, 46364998, 46487196, 46598890, 46658128, 46733170, 46897452, 47461050, 47843518, 47879365, 48176145, 48571290, 48590950, 48615988, 48645972, 48670960, 48914590, 49017600, 49293756, 49495050, 49605952, 49698054, 51094435, 51096339, 51160995, 51208605, 51259635, 51287665, 51341962, 51492753, 51504921, 51590430, 51680799, 51688390, 51759000, 51760962, 51794680, 51877980, 51936880, 51976120, 52357396, 52364875, 52719975, 52816050, 53129700, 53199468, 53387491.

Some larger examples :