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admirable n.  and  nialpdrome

First numbers that belong to both sets:

20, 30, 40, 42, 54, 66, 70, 84, 88, 222, 532, 642, 644, 650, 654, 762, 822, 942, 992, 5322, 5442, 6200, 6522, 6654, 7422, 7532, 7554, 7662, 8432, 8754, 8764, 8876, 8886, 9555, 9642, 9654, 9762, 9772, 9822, 9884, 9942, 53322, 55542, 66522, 72222, 76542, 77442, 77744, 77754, 86322, 86442, 86622, 87222, 87332, 87762, 87774, 88422, 88554, 88732, 94422, 94444, 95322, 95442, 96522, 96666, 98862, 98886, 99642, 99652, 99942, 99966, 99988, 522222, 544310, 554322, 633332, 653322, 654222, 654332, 666654, 743322, 754422, 755322, 762222, 774222, 777522, 777642, 777644, 777774, 843332, 855222, 864222, 864332, 865554, 866442, 887622, 888882, 933222, 942222, 955444, 965442, 966522, 966532, 977442, 977622, 977732, 985552, 986322, 987522, 987762, 988854, 988876, 995322, 997422, 997554, 998742, 999654, 999762, 999942, 3222222, 4444422, 5333322, 5532222, 5544222, 6633222, 6653332, 6655542, 6665322, 6666522, 7332222, 7422222, 7444444, 7654422, 7664322, 7754322, 7755522, 7764222, 7766444, 7774422, 7776222, 7776654, 7777662, 7777722, 8322222, 8333322, 8442222, 8543332, 8644422, 8665422, 8666644, 8753332, 8755554, 8764422, 8765322, 8772222, 8774444, 8776554, 8777742, 8844222, 8854422, 8866542, 8873322, 8876622, 8877764, 8885442, 8887542, 8887732, 8888322, 8888852, 8888862, 9222222, 9554322, 9555532, 9644442, 9654222, 9663222, 9665322, 9666544, 9744222, 9765222, 9765532, 9775554, 9777522, 9866332, 9866622, 9873222, 9873332, 9875442, 9876642, 9876666, 9877422, 9877722, 9884442, 9887322, 9887444, 9887622, 9887754, 9888752, 9888844, 9942222, 9966666, 9976422, 9976542, 9977754, 9977766, 9986322, 9986442, 9986622, 9987762, 9988842, 9995442, 9996222, 9996666, 9997422, 9998322, 9998862, 9998884, 9998886, 9999642, 9999762, 9999942, 43332222, 44433222, 55422222, 55555444, 63333222, 64332222, 65544332, 66554322, 66555222, 66633222, 66642222, 66644322, 66654222, 66665442, 74444442, 75543222, 75554322, 75555222, 76533222, 76653222, 77444322, 77555442, 77643222, 77665542, 77742222, 77755422, 77776554, 84443322, 85555542, 86543322, 86555442, 86633322, 86652222, 86665542, 86666322, 87554442, 87555522, 87642222, 87666666, 87755444, 87764442, 87766532, 87776322, 87777642, 88553332, 88665222, 88666554, 88763322, 88763332, 88773222, 88776654, 88777552, 88854332, 88864422, 88866222, 88866642, 88876542, 88877622, 88877766.

Some larger examples :