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self n.  and  zygodrome

First numbers that belong to both sets:

222, 1111, 1122, 1133, 1144, 1155, 1166, 1177, 1188, 1199, 2200, 2211, 22999, 33000, 33777, 44555, 55333, 55500, 55511, 55522, 77111, 88833, 88844, 88855, 88866, 88877, 88888, 88899, 99666, 110033, 110044, 110055, 110066, 110077, 110088, 110099, 111100, 111111, 222000, 222777, 333444, 339933, 339944, 339955, 339966, 339977, 339988, 339999, 440000, 440011, 448833, 448844, 448855, 448866, 448877, 448888, 448899, 449900, 449911, 449922, 449933, 555999, 557733, 557744, 557755, 557766, 557777, 557788, 557799, 558800, 558811, 558822, 558833, 666633, 666644, 666655, 666666, 666677, 666688, 666699, 667700, 667711, 667722, 667733, 775533, 775544, 775555, 775566, 775577, 775588, 775599, 776600, 776611, 776622, 776633, 777333, 884433, 884444, 884455, 884466, 884477, 884488, 884499, 885500, 885511, 885522, 885533, 888222, 993333, 993344, 993355, 993366, 993377, 993388, 993399, 994400, 994411, 994422, 994433, 999888, 1100044, 1100055, 1100066, 1100077, 1100088, 1100099, 1111999, 1115522, 1115533, 1115544, 1115555, 1115566, 1115577, 1115588, 1115599, 1116600, 1116611, 1116622, 1122000, 1122777, 1133555, 1144333, 1166111, 1177888, 1188666, 1188800, 1188811, 1188822, 1188833, 1199444, 2200999, 2211000, 2211777, 2222555, 2229933, 2229944, 2229955, 2229966, 2229977, 2229988, 2229999, 2233322, 2233333, 2233344, 2233355, 2233366, 2233377, 2233388, 2233399, 2255111, 2266888, 2277666, 2288444, 3300777, 3311555, 3322333, 3332222, 3332233, 3332244, 3332255, 3332266, 3332277, 3332288, 3332299, 3333300, 3333311, 3333322, 3344111, 3355888, 3366633, 3366644, 3366655, 3366666, 3366677, 3366688, 3366699, 3377444, 3399222, 4400555, 4411333, 4433111, 4444888, 4446633, 4446644, 4446655, 4446666, 4446677, 4446688, 4446699, 4447700, 4447711, 4447722, 4447733, 4455666, 4466444, 4466600, 4466611, 4466622, 4466633, 4488222, 4499944, 4499955, 4499966, 4499977, 4499988, 4499999, 5500000, 5500011, 5500333, 5511122, 5511133, 5511144, 5511155, 5511166, 5511177, 5511188, 5511199, 5522111, 5533888, 5544666, 5555444, 5577222, 5588999, 5599000, 5599777, 5599900, 5599911, 5599922, 5599933, 5599944, 6611100, 6611111, 6611122, 6622888, 6633666, 6644433, 6644444, 6644455, 6644466, 6644477, 6644488, 6644499, 6663333, 6663344, 6663355, 6663366, 6663377, 6663388, 6663399, 6664400, 6664411, 6664422, 6664433, 6666222, 6677999, 6688000, 6688777, 6699555, 7700111, 7711888.

Some larger examples :