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balanced n.  and  happy n.

First numbers that belong to both sets:

10, 19, 44, 49, 139, 226, 302, 563, 565, 566, 617, 622, 632, 653, 665, 694, 709, 716, 790, 793, 806, 818, 820, 899, 901, 913, 932, 964, 970, 1366, 1478, 1670, 1758, 2109, 2151, 2157, 2158, 2199, 2206, 2221, 2254, 2275, 2331, 2333, 2390, 2393, 2396, 2417, 2457, 2458, 2484, 2542, 2575, 2582, 2586, 2603, 2620, 2714, 2725, 2755, 2800, 2844, 2851, 2854, 2865, 2910, 2930, 3010, 3123, 3130, 3132, 3173, 3213, 3238, 3269, 3312, 3356, 3365, 3380, 3465, 3466, 3536, 3605, 3634, 3653, 3654, 3736, 3760, 3860, 3920, 3970, 6719, 6791, 6983, 6989, 7039, 7117, 7145, 7225, 7241, 7251, 7255, 7397, 7475, 7521, 7525, 7793, 7841, 7851, 7959, 7983, 7995, 8063, 8125, 8147, 8151, 8175, 8215, 8245, 8247, 8303, 8323, 8379, 8407, 8411, 8414, 8427, 8441, 8442, 8487, 8521, 8542, 8555, 8571, 8597, 8600, 8603, 8630, 8679, 8697, 8751, 8759, 8795, 8801, 8811, 8821, 8847, 8877, 8909, 8937, 8957, 8969, 8975, 8990, 9013, 9031, 9037, 9046, 9073, 9102, 9129, 9130, 9176, 9192, 9263, 9307, 9310, 9323, 9326, 9331, 9387, 9459, 9460, 9495, 9549, 9578, 9638, 9698, 9700, 9758, 9773, 9785, 9786, 9829, 9836, 9863, 9867, 9869, 9875, 9908, 9912, 9954, 9968, 10003, 10009, 10033, 10088, 10115, 10121, 10122, 10148, 10152, 10177, 10184, 10257, 10275, 10281, 10299, 10333, 10373, 10411, 10457, 10474, 10481, 10484, 10511, 10521, 10547, 10574, 10575, 10581, 10582, 10666, 10697, 10706, 10724, 10725, 10755, 10812, 10841, 10844, 10851, 10857, 10881, 10902, 10929, 10930, 10992, 11015, 11021, 11022, 11041, 11051, 11052, 11058, 11077, 11082, 11084, 11085, 11105, 11113, 11120, 11131, 11142, 11143, 11145, 11154, 11195, 11201, 11202, 11208, 11220, 11229, 11232, 11243, 11251, 11267, 11283, 11294, 11322, 11324, 11341, 11342, 11377, 11384, 11385, 11413, 11415, 11417, 11429.

Some larger examples :