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Harshad n.  and  nialpdrome

First numbers that belong to both sets:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 21, 30, 40, 42, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 110, 111, 200, 210, 220, 222, 300, 320, 322, 330, 333, 400, 410, 420, 432, 440, 441, 444, 500, 510, 511, 522, 531, 540, 550, 552, 555, 600, 621, 630, 640, 644, 660, 666, 700, 711, 720, 730, 732, 770, 774, 777, 800, 810, 820, 832, 840, 864, 870, 874, 880, 882, 888, 900, 910, 954, 960, 966, 972, 990, 999, 1100, 1110, 2000, 2100, 2200, 2210, 2220, 3000, 3100, 3110, 3200, 3210, 3220, 3222, 3300, 3320, 3321, 3330, 4000, 4100, 4110, 4200, 4221, 4311, 4320, 4330, 4332, 4400, 4410, 4420, 4440, 5000, 5100, 5110, 5211, 5220, 5310, 5320, 5400, 5410, 5432, 5500, 5520, 5544, 5550, 6000, 6111, 6200, 6210, 6220, 6300, 6310, 6331, 6400, 6420, 6440, 6443, 6444, 6540, 6552, 6600, 6630, 6640, 6642, 6660, 7000, 7110, 7200, 7210, 7300, 7320, 7322, 7440, 7500, 7530, 7542, 7543, 7620, 7632, 7644, 7650, 7700, 7710, 7722, 7740, 7744, 7760, 7770, 7776, 8000, 8100, 8110, 8200, 8220, 8320, 8330, 8400, 8430, 8432, 8442, 8520, 8532, 8550, 8610, 8622, 8640, 8652, 8660, 8664, 8700, 8730, 8740, 8775, 8800, 8820, 8840, 8841, 8880, 8883, 9000, 9100, 9300, 9330, 9420, 9432, 9510, 9520, 9522, 9540, 9600, 9630, 9660, 9666, 9720, 9740, 9744, 9752, 9774, 9810, 9854, 9855, 9882, 9900, 9920, 9922, 9960, 9963, 9990, 10000, 11000, 11100, 20000, 21000, 21100, 21110, 22000, 22100, 22110, 22200, 22221, 30000, 31000, 31100, 31110, 32000, 32100, 32200, 32211, 32220, 33000, 33111, 33200, 33210, 33220, 33300, 33310, 40000, 41000, 41100, 42000, 42111, 42200, 42210, 42220, 43110, 43200, 43210, 43300, 43320, 44000, 44100, 44110, 44200.

Some larger examples :