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happy n.  and  nialpdrome

First numbers that belong to both sets:

1, 7, 10, 31, 32, 44, 70, 82, 86, 91, 94, 97, 100, 310, 320, 331, 440, 622, 632, 644, 653, 655, 665, 700, 761, 763, 820, 833, 860, 863, 874, 881, 888, 910, 921, 931, 932, 940, 964, 970, 973, 998, 1000, 2111, 2211, 2221, 3100, 3200, 3310, 3321, 3331, 3332, 4111, 4222, 4400, 4441, 5111, 5211, 5331, 5422, 5533, 5542, 5544, 5552, 5554, 5555, 6220, 6320, 6433, 6440, 6530, 6533, 6543, 6550, 6631, 6643, 6650, 6661, 6665, 7000, 7331, 7421, 7441, 7444, 7521, 7522, 7541, 7542, 7551, 7552, 7610, 7630, 7633, 7663, 7711, 7721, 7744, 7754, 8200, 8211, 8330, 8332, 8333, 8411, 8441, 8442, 8511, 8521, 8522, 8542, 8554, 8555, 8600, 8630, 8652, 8740, 8741, 8742, 8751, 8810, 8811, 8821, 8874, 8877, 8880, 8881, 8884, 9100, 9210, 9310, 9320, 9331, 9332, 9400, 9444, 9632, 9640, 9655, 9700, 9730, 9761, 9773, 9863, 9873, 9875, 9876, 9921, 9951, 9954, 9975, 9980, 9982, 9986, 10000, 21110, 22110, 22210, 31000, 31111, 32000, 32211, 33100, 33210, 33310, 33320, 33321, 41110, 42111, 42220, 42222, 43111, 43211, 43331, 44000, 44222, 44322, 44410, 44442, 51110, 52110, 52111, 53310, 54111, 54220, 54333, 54432, 54443, 55330, 55411, 55420, 55432, 55440, 55442, 55443, 55520, 55540, 55543, 55550, 55553, 62200, 62221, 63200, 64330, 64333, 64400, 64411, 64433, 64444, 65221, 65300, 65330, 65411, 65421, 65430, 65441, 65442, 65444, 65500, 65521, 65522, 65541, 66310, 66321, 66331, 66332, 66430, 66500, 66544, 66610, 66643, 66650, 70000, 73222, 73310, 74111, 74210, 74321, 74322, 74410, 74421, 74431, 74432, 74440, 75210, 75220, 75222, 75322, 75410, 75420, 75431, 75432, 75510, 75520, 75531, 75553, 76100, 76211, 76221, 76222, 76300, 76330, 76411, 76422, 76444, 76542, 76552, 76622, 76630, 76633, 76666, 77110, 77210, 77311, 77440, 77443, 77531, 77540, 77621, 77742, 77752.

Some larger examples :