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balanced n.  and  nialpdrome

First numbers that belong to both sets:

2, 9, 10, 11, 21, 41, 42, 44, 50, 52, 75, 99, 210, 332, 410, 420, 500, 520, 532, 541, 542, 544, 550, 551, 552, 555, 600, 611, 620, 622, 630, 632, 651, 652, 653, 654, 660, 661, 662, 665, 666, 710, 721, 722, 740, 742, 744, 752, 775, 810, 820, 841, 842, 844, 850, 852, 865, 866, 872, 880, 920, 930, 932, 944, 954, 961, 962, 964, 970, 976, 990, 992, 1110, 2110, 2221, 2222, 3111, 3211, 3221, 3222, 3300, 4000, 7433, 7511, 7521, 7611, 7751, 7755, 8311, 8321, 8331, 8410, 8411, 8430, 8431, 8441, 8442, 8443, 8444, 8510, 8521, 8530, 8541, 8542, 8543, 8551, 8553, 8555, 8600, 8620, 8621, 8622, 8630, 8631, 8633, 8641, 8643, 8651, 8653, 8654, 8661, 8662, 8665, 8666, 8751, 8763, 8765, 8766, 8811, 8821, 8822, 8840, 8855, 8861, 8862, 8871, 8875, 8877, 8883, 8885, 8886, 9110, 9200, 9310, 9331, 9333, 9411, 9421, 9422, 9430, 9433, 9441, 9443, 9511, 9530, 9532, 9543, 9550, 9551, 9555, 9611, 9621, 9622, 9641, 9642, 9644, 9650, 9652, 9663, 9700, 9711, 9743, 9751, 9755, 9771, 9773, 9774, 9811, 9820, 9830, 9833, 9841, 9842, 9844, 9863, 9870, 9875, 9877, 9881, 9882, 9884, 9900, 9930, 9932, 9940, 9944, 9953, 9954, 9960, 9971, 9983, 9987, 9991, 9995, 9997, 9998, 11111, 33211, 42211, 42220, 43000, 43111, 43210, 43211, 43221, 43222, 43310, 43321, 43322, 44000, 44110, 44210, 44300, 44310, 44330, 44332, 44400, 44421, 44422, 44433, 44440, 51000, 53310, 54000, 54100, 54210, 54311, 54330, 54332, 54411, 54421, 54422, 54441, 54442, 54444, 55200, 55311, 55410, 55431, 55443, 55500, 55521, 55522, 61000, 62100, 62211, 62220, 63000, 64320, 211100, 211110, 220000, 222000, 222100, 310000, 322000, 322200, 332100, 333000, 333210, 421110, 432000, 433322, 440000, 441110, 443211, 444420, 521100, 522000, 522210.

Some larger examples :