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congruent n.  and  nude n.

First numbers that belong to both sets:

5, 6, 7, 15, 22, 24, 55, 77, 88, 111, 112, 124, 126, 135, 175, 184, 212, 216, 222, 224, 244, 248, 312, 333, 336, 366, 384, 412, 444, 448, 624, 636, 728, 735, 777, 824, 848, 864, 888, 999, 1111, 1112, 1113, 1116, 1122, 1131, 1144, 1155, 1164, 1176, 1197, 1212, 1222, 1224, 1236, 1244, 1248, 1311, 1326, 1332, 1335, 1344, 1368, 1412, 1464, 1488, 1575, 1632, 1662, 1692, 1848, 1888, 1926, 1935, 1944, 2128, 2136, 2144, 2166, 2184, 2196, 2222, 2232, 2244, 2262, 2288, 2328, 2364, 2424, 2436, 2488, 2616, 2622, 2744, 2772, 3111, 3126, 3132, 3135, 3168, 3171, 3222, 3288, 3312, 3324, 3333, 3339, 3366, 3384, 3444, 3555, 3612, 3636, 3717, 3864, 3924, 3933, 3996, 4112, 4116, 4124, 4184, 4212, 4244, 4248, 4344, 4412, 4416, 4444, 4448, 4464, 4488, 4632, 4824, 4848, 4888, 4896, 4932, 4968, 5115, 5535, 5775, 6126, 6132, 6144, 6168, 6222, 6264, 6324, 6366, 6384, 6612, 6624, 6636, 6648, 6762, 6816, 6864, 6966, 6984, 7119, 7175, 7224, 7448, 7476, 7644, 8128, 8136, 8144, 8184, 8224, 8248, 8288, 8616, 8664, 8688, 8736, 8824, 8832, 8888, 8928, 9126, 9135, 9144, 9333, 9396, 9432, 9936, 9999, 11111, 11124, 11128, 11133, 11136, 11166, 11196, 11222, 11224, 11226, 11232, 11248, 11262, 11288, 11316, 11412, 11444, 11448, 11488, 11535, 11616, 11622, 11676, 11711, 11832, 11872, 11888, 12112, 12124, 12126, 12128, 12144, 12184, 12212, 12216, 12222, 12224, 12244, 12248, 12312, 12324, 12366, 12384, 12412, 12432, 12444, 12488, 12624, 12636, 12726, 12768, 12824, 12888, 12924, 13116, 13212, 13236, 13248, 13272, 13311, 13326, 13332, 13335, 13362, 13368, 13392, 13464, 13515, 13632, 13662, 13776, 13797, 13824, 13848, 13896, 14136, 14144, 14224, 14232, 14288, 14292, 14328, 14364, 14412, 14424, 14448, 14488, 14616, 14688, 14784, 14832.

Some larger examples :