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modest n.  and  zygodrome

First numbers that belong to both sets:

111, 222, 333, 444, 555, 666, 777, 888, 999, 1111, 1133, 1199, 2222, 2233, 2266, 2299, 3333, 3399, 4444, 4466, 4499, 5555, 5599, 6666, 6699, 7777, 7799, 8888, 8899, 9999, 11111, 11333, 11999, 22111, 22222, 22333, 22666, 22999, 33111, 33333, 33999, 44111, 44222, 44333, 44444, 44666, 44999, 55111, 55333, 55555, 55999, 66111, 66222, 66333, 66666, 66999, 77111, 77333, 77777, 77999, 88111, 88222, 88333, 88444, 88666, 88888, 88999, 99111, 99333, 99999, 110033, 110099, 111111, 111333, 111999, 112222, 113333, 115555, 116666, 119999, 220033, 220066, 220099, 221111, 222222, 222333, 222666, 222999, 223333, 224444, 225555, 226666, 229999, 330099, 331111, 333333, 333999, 335555, 336666, 339999, 440066, 440099, 441111, 442222, 443333, 444444, 444666, 444999, 445555, 446666, 448888, 449999, 550099, 551111, 553333, 555555, 555999, 556666, 559999, 660099, 661111, 662222, 663333, 666666, 666999, 669999, 770099, 771111, 773333, 777777, 777999, 779999, 880099, 881111, 882222, 883333, 884444, 886666, 888888, 888999, 889999, 991111, 993333, 999999, 1100033, 1100099, 1111111, 1113333, 1119999, 1122222, 1133333, 1155555, 1166666, 1199999, 2200033, 2200066, 2200099, 2211111, 2221111, 2222222, 2223333, 2226666, 2229999, 2233333, 2244444, 2255555, 2266666, 2299999, 3300099, 3311111, 3322222, 3331111, 3333333, 3339999, 3355555, 3366666, 3399999, 4400066, 4400099, 4411111, 4422222, 4433333, 4441111, 4441188, 4442222, 4443333, 4444444, 4446666, 4449999, 4455555, 4466666, 4488888, 4499999, 5500099, 5511111, 5522222, 5522277, 5533333, 5551111, 5553333, 5555555, 5559999, 5566666, 5599999, 6600099, 6611111, 6622222, 6633333, 6644444, 6655555, 6661111, 6662222, 6663333, 6666666, 6669999, 6699999, 7700099, 7711111, 7722222, 7733333, 7755555, 7766666, 7771111, 7773333, 7777777, 7779999, 7799999, 8800099, 8811111, 8822222, 8833333, 8844444, 8855555, 8866666, 8881111, 8881188, 8882222, 8883333, 8884444, 8886666, 8888888, 8889999, 8899999, 9911111, 9922222, 9933333, 9955555, 9966666, 9991111, 9993333, 9999999, 11000033, 11000077, 11000099, 11000111, 11000333, 11000777, 11000999, 11001111, 11002222, 11002255, 11003300, 11003333, 11004444, 11004477, 11005555, 11006666, 11009900, 11009999, 11100333, 11100999, 11111111, 11113333, 11119999, 11122222, 11133333, 11155555, 11166666, 11199999, 11222222.

Some larger examples :