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arithmetic n.  and  nude n.

First numbers that belong to both sets:

1, 3, 5, 6, 7, 11, 15, 22, 33, 44, 55, 66, 77, 99, 111, 115, 126, 132, 135, 155, 168, 184, 212, 222, 224, 248, 264, 315, 366, 432, 515, 555, 612, 636, 672, 728, 735, 777, 824, 864, 999, 1111, 1113, 1115, 1122, 1124, 1128, 1131, 1155, 1212, 1222, 1244, 1248, 1266, 1288, 1311, 1326, 1335, 1362, 1395, 1412, 1416, 1424, 1515, 1555, 1626, 1632, 1644, 1662, 1715, 1722, 1771, 1824, 1848, 1888, 1926, 1935, 2128, 2144, 2166, 2184, 2222, 2224, 2226, 2232, 2244, 2262, 2322, 2364, 2436, 2444, 2488, 2622, 2688, 2744, 2832, 3111, 3126, 3132, 3135, 3144, 3162, 3168, 3171, 3195, 3222, 3315, 3333, 3336, 3339, 3366, 3384, 3393, 3432, 3444, 3555, 3624, 3666, 3717, 3864, 3915, 3933, 4124, 4128, 4164, 4172, 4236, 4244, 4412, 4424, 4444, 4448, 4488, 4872, 4888, 4968, 5115, 5155, 5355, 5515, 5535, 5555, 5775, 6126, 6162, 6216, 6222, 6312, 6324, 6366, 6384, 6432, 6444, 6612, 6624, 6666, 6696, 6762, 6816, 6888, 7112, 7119, 7175, 7224, 7266, 7476, 7777, 7784, 8144, 8184, 8232, 8248, 8288, 8328, 8496, 8616, 8736, 8824, 8832, 8848, 8928, 9126, 9135, 9144, 9288, 9333, 9396, 9612, 9666, 9936, 9999, 11111, 11112, 11115, 11122, 11144, 11155, 11166, 11222, 11224, 11226, 11232, 11248, 11262, 11313, 11316, 11331, 11355, 11364, 11424, 11436, 11444, 11488, 11515, 11535, 11555, 11616, 11622, 11688, 11711, 11824, 11872, 12122, 12126, 12128, 12162, 12212, 12222, 12264, 12366, 12384, 12412, 12444, 12488, 12648, 12666, 12712, 12726, 12768, 12816, 12824, 12924, 13113, 13128, 13155, 13164, 13224, 13236, 13266, 13272, 13311, 13326, 13332, 13335, 13344, 13362, 13377, 13392, 13416, 13515, 13662, 13713, 13755, 13797, 13824, 13995, 14124, 14136, 14144, 14212, 14244, 14288, 14316, 14328, 14444, 14616, 14664, 14688, 14728, 15115.

Some larger examples :