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balanced n.  and  self n.

First numbers that belong to both sets:

9, 42, 75, 108, 154, 165, 198, 209, 266, 312, 424, 468, 558, 569, 602, 613, 626, 659, 681, 692, 714, 716, 738, 782, 793, 817, 850, 872, 894, 905, 916, 929, 962, 1054, 1210, 1346, 2022, 2110, 2134, 2268, 2290, 2347, 2358, 2402, 2426, 2470, 2481, 2514, 2516, 2538, 2582, 2617, 2650, 2661, 2716, 2729, 2740, 2762, 2830, 2841, 2885, 2920, 2953, 2964, 3111, 3157, 3214, 3225, 3269, 3370, 3416, 3504, 3528, 3605, 3640, 3651, 3684, 3717, 3730, 3752, 3864, 3908, 3976, 6799, 6911, 7001, 7027, 7115, 7117, 7251, 7273, 7475, 7521, 7767, 7811, 7835, 8151, 8173, 8195, 8219, 8285, 8318, 8331, 8375, 8443, 8487, 8509, 8555, 8566, 8599, 8621, 8634, 8678, 8689, 8735, 8801, 8825, 8847, 8891, 8924, 8937, 8948, 9003, 9014, 9062, 9073, 9095, 9130, 9185, 9275, 9319, 9387, 9398, 9422, 9433, 9499, 9523, 9578, 9611, 9622, 9635, 9712, 9758, 9813, 9848, 9870, 9881, 9925, 9938, 9960, 9971, 10054, 10065, 10122, 10177, 10223, 10267, 10311, 10357, 10379, 10401, 10414, 10425, 10458, 10469, 10526, 10570, 10581, 10616, 10638, 10649, 10693, 10728, 10805, 10829, 10851, 10906, 10917, 10930, 10985, 11022, 11033, 11077, 11112, 11145, 11156, 11200, 11213, 11279, 11347, 11369, 11380, 11413, 11415, 11437, 11448, 11459, 11470, 11492, 11527, 11560, 11593, 11604, 11617, 11672, 11716, 11729, 11795, 11817, 11841, 11852, 11874, 11907, 11931, 12056, 12100, 12157, 12168, 12179, 12280, 12313, 12315, 12381, 12403, 12427, 12493, 12515, 12517, 12583, 12605, 12629, 12651, 12719, 12741, 12807, 12820, 12853, 12875, 12886, 12908, 12954, 12965, 12987, 12998, 13009, 13112, 13125, 13202, 13327, 13404, 13415, 13417, 13428, 13461, 13505, 13516, 13540, 13573, 13606, 13617, 13641, 13652, 13685, 13720, 13731, 13753, 13764, 13843, 13865, 13876, 13898, 13922, 13955, 13988, 14047, 14113, 14115, 14148, 14159, 14216.

Some larger examples :