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Harshad n.  and  zygodrome

First numbers that belong to both sets:

111, 222, 333, 444, 555, 666, 777, 888, 999, 1100, 1122, 1188, 2200, 2244, 3300, 3366, 3388, 4400, 4488, 5500, 5544, 5566, 6600, 7700, 7722, 7744, 8800, 9900, 9922, 11000, 11100, 11133, 22000, 22200, 22266, 33000, 33111, 33300, 33399, 33444, 33777, 44000, 44400, 55000, 55500, 55566, 66000, 66222, 66555, 66600, 66888, 77000, 77700, 77733, 88000, 88800, 99000, 99333, 99900, 110000, 110022, 110088, 111000, 111100, 111144, 111222, 111888, 112200, 112266, 112288, 113344, 114400, 114422, 114444, 114466, 115500, 116622, 116644, 117744, 118800, 118822, 119900, 119988, 220000, 220044, 221100, 221144, 221166, 221188, 222000, 222111, 222200, 222288, 222444, 222777, 223300, 223344, 223366, 224400, 225522, 225544, 226688, 227700, 227722, 228800, 228844, 228888, 229900, 330000, 330066, 330088, 332200, 332244, 332266, 333000, 333300, 333666, 334422, 334444, 335544, 336600, 336622, 337700, 337788, 338800, 440000, 440088, 441100, 441144, 441166, 442200, 442288, 443322, 443344, 444000, 444222, 444400, 444555, 444888, 445500, 445522, 446600, 446688, 447700, 448800, 449988, 550000, 550044, 550066, 551100, 552222, 552244, 552266, 553344, 554400, 554422, 555000, 555444, 555500, 555588, 556600, 558866, 559944, 559988, 660000, 661122, 661144, 663300, 663322, 664400, 664488, 665500, 665522, 666000, 666333, 666600, 668844, 668888, 669900, 770000, 770022, 770044, 771144, 772200, 772222, 773300, 773388, 774400, 777000, 777222, 777700, 777744, 777788, 778800, 880000, 881100, 881122, 882200, 882288, 883300, 884400, 886644, 886688, 887700, 888000, 888111, 888444, 888800, 889922, 990000, 990022, 991100, 991144, 991188, 992200, 993344, 995544, 995588, 996600, 998844, 999000, 999900, 999944, 1100000, 1100022, 1100088, 1110000, 1110033, 1111000, 1111100, 1111122, 1111155, 1111177, 1111199, 1112211, 1113300, 1113399, 1114499, 1116600, 1116611, 1116633, 1116666, 1119933, 1122000, 1122111, 1122200, 1122288, 1122444, 1122555, 1133000, 1133555, 1133888, 1144000, 1144422, 1155000, 1155222, 1155888, 1155999, 1166600, 1166688, 1188000, 1188844, 1199000, 1199555, 2200000, 2200044, 2211000, 2211111, 2211444, 2220000, 2220066, 2222000, 2222200, 2222244, 2223300, 2224422, 2225544, 2226600, 2227700, 2227788.

Some larger examples :