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congruent n.  and  zygodrome

First numbers that belong to both sets:

22, 55, 77, 88, 111, 222, 333, 444, 777, 888, 999, 1111, 1122, 1133, 1144, 1155, 1166, 1199, 2200, 2222, 2244, 2255, 2277, 2288, 3311, 3333, 3355, 3366, 3388, 3399, 4411, 4422, 4444, 4455, 4466, 4477, 4488, 5500, 5511, 5533, 5544, 5566, 5588, 5599, 6622, 6644, 6655, 6677, 7700, 7711, 7733, 7766, 7799, 8800, 8822, 8855, 8866, 8877, 8888, 9911, 9933, 9944, 9966, 9999, 11000, 11100, 11111, 11133, 11166, 11188, 11199, 11222, 11333, 11444, 11888, 11999, 22000, 22111, 22200, 22211, 22222, 22255, 22277, 22288, 22333, 22999, 33000, 33111, 33222, 33300, 33311, 33333, 33366, 33399, 33888, 33999, 44000, 44111, 44222, 44333, 44400, 44422, 44444, 44455, 44477, 44888, 44999, 55000, 55111, 55222, 55333, 55444, 55511, 55522, 55533, 55544, 55555, 55566, 55599, 55888, 55999, 66000, 66111, 66222, 66333, 66555, 66622, 66633, 66644, 66655, 66677, 66888, 66999, 77111, 77222, 77333, 77700, 77711, 77733, 77766, 77788, 77799, 77888, 77999, 88000, 88111, 88222, 88333, 88444, 88800, 88822, 88844, 88855, 88877, 88888, 88999, 99000, 99111, 99222, 99333, 99444, 99666, 99900, 99911, 99933, 99966, 99977, 99988, 99999, 110022, 110044, 110055, 110077, 111000, 111100, 111111, 111133, 111155, 111166, 111188, 111199, 111222, 111333, 111444, 111888, 111999, 112200, 112222, 112244, 112255, 112266, 112277, 112299, 113300, 113311, 113333, 113355, 113366, 113399, 114400, 114422, 114455, 114477, 114488, 115500, 115511, 115533, 115544, 115566, 115588, 115599, 116600, 116622, 116655, 116677, 116688, 117711, 117733, 117744, 117766, 117788, 117799, 118822, 118844, 118855, 118877, 119900, 119911, 119922, 119933, 119944, 119966, 119988, 119999, 220000, 220022, 220055, 220066, 220077, 220088, 221111, 221133, 221144, 221166, 221188, 221199, 222111, 222200, 222222, 222255, 222277, 222288, 222333, 222555, 222666, 222999, 223311, 223333, 223344, 223355, 223366, 223388, 223399, 224400, 224422, 224444, 224455, 224477, 225500, 225511, 225533, 225566, 225588, 225599, 226622, 226644, 226655, 226677, 226688, 227700.

Some larger examples :