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junction n.  and  zygodrome

First numbers that belong to both sets:

111, 3322, 4422, 5522, 6622, 7722, 8822, 9922, 11111, 22111, 22222, 33111, 33222, 33311, 44111, 44222, 44422, 55111, 55222, 66222, 66622, 77222, 77333, 77733, 88222, 88333, 99222, 99333, 99933, 112222, 113322, 114422, 115522, 116622, 117722, 118822, 119922, 220022, 221122, 222111, 222222, 223322, 224422, 225522, 226622, 227722, 228822, 229922, 330022, 331122, 332222, 333322, 334422, 335522, 336622, 337722, 338822, 441122, 442222, 443322, 444222, 444422, 445522, 446622, 447722, 550022, 550033, 550044, 551122, 552222, 553322, 554422, 555522, 556622, 559944, 660022, 660033, 660044, 661122, 662222, 663322, 664422, 665522, 666222, 666333, 668844, 669944, 770022, 770033, 770044, 771122, 772222, 773322, 774422, 777744, 778844, 779944, 880022, 880033, 880044, 881122, 882222, 883322, 886644, 887744, 888333, 888444, 888844, 889944, 990022, 990033, 990044, 991122, 992222, 995544, 996644, 997744, 998844, 999944, 1100111, 1110011, 1110022, 1110033, 1111111, 1111222, 1112211, 1113311, 1114411, 1117733, 1118833, 1119933, 1122111, 1122222, 1133111, 1133222, 1133311, 1144111, 1144222, 1144422, 1155222, 1155533, 1166222, 1166333, 1166622, 1177222, 1177333, 1177733, 1188222, 1188333, 1199222, 1199333, 1199933, 2200022, 2200033, 2200111, 2200222, 2211111, 2211222, 2220022, 2221122, 2222111, 2222222, 2223322, 2224422, 2225522, 2226622, 2227722, 2228822, 2233111, 2233222, 2244222, 2244422, 2255222, 2255333, 2255533, 2266222, 2266333, 2266622, 2277222, 2277333, 2277733, 2288222, 2288333, 2288844, 2299333, 2299933, 3300022, 3300033, 3300111, 3300222, 3311111, 3311222, 3322111, 3322222, 3330011, 3330022, 3330033, 3331111, 3333222, 3334433, 3335533, 3336633, 3337733, 3338833, 3339933, 3344222, 3344333, 3344422, 3355222, 3355333, 3355533, 3366222, 3366333, 3377222, 3377333, 3377733, 3388333, 3388844, 3399333, 3399444, 3399933, 4400022, 4400033, 4400111, 4400222, 4411111, 4411222, 4422222, 4433222, 4433333, 4440022, 4440033, 4440044, 4441122, 4442222, 4443322, 4444222, 4444333, 4444422, 4445522, 4448844, 4449944, 4455222, 4455333, 4455533, 4466222, 4466333, 4477333, 4477733, 4488333, 4488444, 4488844, 4499333, 4499444, 5500111, 5500222, 5511222, 5522222, 5522333, 5533222, 5533333, 5544222, 5544333, 5544422, 5550033, 5551133, 5552233, 5553333, 5554433, 5555222, 5555333, 5555533, 5556633, 5557733, 5558833, 5559933, 5566333, 5566644, 5577333, 5577444.

Some larger examples :