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modest n.  and  nude n.

First numbers that belong to both sets:

111, 222, 333, 412, 444, 515, 555, 666, 777, 824, 888, 999, 1111, 1222, 1236, 1244, 1266, 1555, 1644, 2222, 2436, 2444, 2488, 3111, 3288, 3333, 3555, 3666, 4444, 4872, 4888, 5555, 6162, 6222, 6666, 7777, 8888, 9333, 9999, 11111, 12162, 12222, 12324, 12444, 12666, 15135, 15555, 22222, 24216, 24324, 24444, 24648, 24888, 33111, 33333, 36162, 36222, 36324, 36444, 36666, 41212, 44444, 48144, 48216, 48432, 48648, 48888, 51515, 55555, 64296, 66162, 66222, 66666, 72324, 77777, 82424, 88888, 96444, 99333, 99999, 111111, 111333, 112144, 112222, 112444, 112888, 115555, 117999, 121212, 122222, 123636, 124444, 126162, 126222, 126666, 128144, 128288, 128888, 131313, 132162, 132222, 132324, 132444, 132666, 135555, 136296, 144216, 144324, 144432, 144444, 144648, 144888, 151515, 155555, 161616, 162222, 162666, 168216, 168648, 168888, 171717, 184888, 192222, 192888, 212222, 212444, 216222, 216324, 216444, 216648, 216666, 216888, 216972, 222222, 222666, 224288, 224444, 224888, 241212, 242424, 243636, 244444, 248888, 262626, 264324, 264444, 264648, 264888, 272888, 276444, 288432, 288648, 288864, 288888, 312324, 312444, 312648, 312666, 312888, 313131, 315555, 323232, 324444, 333333, 333999, 336432, 336444, 336648, 336666, 336888, 353535, 361212, 363636, 366666, 372666, 373737, 384432, 384648, 384864, 384888, 393939, 396666, 412444, 424444, 424888, 432444, 432648, 432888, 441212, 444444, 448888, 482424, 484848, 488888, 515555, 551515, 555555, 612666, 624648, 624888, 626262, 636666, 641616, 646464, 648888, 666666, 696888, 717171, 724444, 727272, 737373, 757575, 767676, 777777, 816888, 824888, 848888, 864888, 882424, 888888, 911313, 924444, 939393, 962424, 969696, 999999, 1111111, 1113333, 1121212, 1121232, 1121616, 1121848, 1122222, 1122424, 1122772, 1124444, 1124848, 1128888, 1131111, 1151515, 1155555, 1164444, 1173333, 1222222, 1241212, 1241364, 1244444, 1266666, 1282112, 1282424, 1283232, 1284224, 1284848, 1287272, 1288888, 1311111, 1321212, 1323636, 1326666, 1331919, 1351515, 1362222, 1368888, 1371111, 1441212, 1441296, 1442424, 1443636, 1444444, 1444848, 1448888, 1551515, 1555115, 1555555, 1626666, 1644444, 1662222, 1681848, 1682424, 1751155.

Some larger examples :