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balanced n.  and  plaindrome

First numbers that belong to both sets:

2, 9, 11, 12, 15, 19, 35, 37, 38, 44, 49, 56, 78, 99, 114, 135, 139, 147, 149, 156, 166, 169, 177, 178, 225, 226, 228, 266, 268, 278, 344, 348, 468, 555, 557, 558, 566, 569, 578, 588, 589, 666, 668, 677, 678, 689, 779, 789, 899, 1138, 1178, 1334, 1346, 1358, 1366, 1478, 1778, 2222, 2226, 2227, 2229, 2233, 2234, 2236, 2247, 2259, 2266, 2268, 2277, 2278, 2289, 2333, 2334, 2347, 2349, 2355, 2357, 2358, 2379, 2389, 2445, 2446, 2457, 2458, 2467, 2469, 2488, 2499, 2558, 2566, 2589, 2599, 2666, 2668, 2678, 2699, 2778, 2788, 2889, 3335, 3339, 3347, 3349, 3356, 3366, 3369, 3377, 3378, 3459, 3466, 3468, 3489, 3666, 3668, 3688, 3777, 3778, 3888, 6799, 7799, 8889, 8999, 11111, 11112, 11113, 11119, 11129, 11135, 11139, 11145, 11146, 11148, 11155, 11156, 11169, 11225, 11229, 11237, 11239, 11247, 11255, 11267, 11279, 11335, 11339, 11345, 11347, 11349, 11355, 11356, 11359, 11366, 11369, 11377, 11378, 11399, 11444, 11448, 11455, 11459, 11466, 11467, 11468, 11469, 11479, 11489, 11555, 11557, 11558, 11559, 11569, 11589, 11666, 11668, 11688, 11689, 11699, 11789, 11888, 11889, 12224, 12233, 12237, 12245, 12249, 12335, 12339, 12347, 12349, 12367, 12379, 12445, 12446, 12455, 12457, 12459, 12467, 12469, 12479, 12489, 12499, 12559, 12567, 12589, 12669, 12679, 12699, 12799, 12889, 12899, 13333, 13335, 13339, 13355, 13357, 13358, 13366, 13369, 13389, 13447, 13459, 13466, 13468, 13469, 13477, 13478, 13489, 13559, 13569, 13579, 13589, 13666, 13668, 13699, 14444, 14447, 14449, 14456, 14477, 14478, 14489, 14499, 14568, 14599, 14666, 14668, 14677, 14689, 14699, 14779, 14788, 14889, 15556, 15568, 15569, 15577, 15599, 15688, 15689, 15777, 15889, 16689, 16789, 16799, 17777, 18999, 23346, 23778, 24456, 24699, 25569, 25779, 25788, 26679, 27789, 33399, 33455, 33467, 33469, 33499.

Some larger examples :