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nialpdrome  and  zygodrome

First numbers that belong to both sets:

11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1100, 1111, 2200, 2211, 2222, 3300, 3311, 3322, 3333, 4400, 4411, 4422, 4433, 4444, 5500, 5511, 5522, 5533, 5544, 5555, 6600, 6611, 6622, 6633, 6644, 6655, 6666, 7700, 7711, 7722, 7733, 7744, 7755, 7766, 7777, 8800, 8811, 8822, 8833, 8844, 8855, 8866, 8877, 8888, 9900, 9911, 9922, 9933, 9944, 9955, 9966, 9977, 9988, 9999, 11000, 11100, 11111, 22000, 22111, 22200, 22211, 22222, 33000, 33111, 33222, 33300, 33311, 33322, 33333, 44000, 44111, 44222, 44333, 44400, 44411, 44422, 44433, 44444, 55000, 55111, 55222, 55333, 55444, 55500, 55511, 55522, 55533, 55544, 55555, 66000, 66111, 66222, 66333, 66444, 66555, 66600, 66611, 66622, 66633, 66644, 66655, 66666, 77000, 77111, 77222, 77333, 77444, 77555, 77666, 77700, 77711, 77722, 77733, 77744, 77755, 77766, 77777, 88000, 88111, 88222, 88333, 88444, 88555, 88666, 88777, 88800, 88811, 88822, 88833, 88844, 88855, 88866, 88877, 88888, 99000, 99111, 99222, 99333, 99444, 99555, 99666, 99777, 99888, 99900, 99911, 99922, 99933, 99944, 99955, 99966, 99977, 99988, 99999, 110000, 111000, 111100, 111111, 220000, 221100, 221111, 222000, 222111, 222200, 222211, 222222, 330000, 331100, 331111, 332200, 332211, 332222, 333000, 333111, 333222, 333300, 333311, 333322, 333333, 440000, 441100, 441111, 442200, 442211, 442222, 443300, 443311, 443322, 443333, 444000, 444111, 444222, 444333, 444400, 444411, 444422, 444433, 444444, 550000, 551100, 551111, 552200, 552211, 552222, 553300, 553311, 553322, 553333, 554400, 554411, 554422, 554433, 554444, 555000, 555111, 555222, 555333, 555444, 555500, 555511, 555522, 555533, 555544, 555555, 660000, 661100, 661111, 662200, 662211, 662222, 663300, 663311, 663322, 663333, 664400, 664411, 664422, 664433, 664444, 665500, 665511, 665522, 665533, 665544, 665555, 666000, 666111, 666222, 666333, 666444, 666555, 666600, 666611, 666622, 666633, 666644, 666655, 666666, 770000, 771100, 771111, 772200, 772211.

Some larger examples :