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happy n.  and  nude n.

First numbers that belong to both sets:

1, 7, 44, 784, 888, 1112, 1115, 1122, 1128, 1184, 1212, 1222, 1288, 1332, 1335, 1444, 1448, 1575, 1771, 1888, 2112, 2122, 2212, 2224, 2448, 3132, 3135, 3312, 3315, 4144, 4172, 4184, 4248, 4824, 4872, 4888, 5555, 8112, 8128, 8144, 8424, 8488, 8848, 11124, 11232, 11248, 11322, 11328, 11412, 11824, 11832, 12132, 12184, 12312, 12366, 12384, 12636, 12726, 12996, 13122, 13128, 13212, 13248, 13266, 13332, 13626, 13662, 13755, 13824, 14112, 14128, 14328, 14832, 16236, 16326, 16362, 16632, 16992, 17262, 17535, 18312, 18432, 19296, 19692, 19926, 19962, 21132, 21184, 21312, 21366, 21384, 21636, 21672, 21996, 22176, 22224, 22244, 22344, 22424, 22764, 23112, 23166, 23184, 23244, 23424, 23448, 23616, 24224, 24276, 24324, 24384, 24432, 24444, 26136, 26316, 26712, 27216, 28344, 29196, 29916, 31122, 31128, 31212, 31248, 31266, 31332, 31626, 31662, 31824, 32112, 32166, 32184, 32244, 32424, 32448, 32616, 33132, 33312, 33768, 34128, 34224, 34248, 34272, 34824, 35175, 36126, 36162, 36216, 36612, 38112, 38424, 41112, 41128, 41328, 41832, 42224, 42324, 42384, 42432, 42444, 42672, 43128, 43224, 43248, 43824, 44232, 44244, 44328, 44424, 44488, 44832, 44848, 47124, 48112, 48312, 48432, 48448, 61236, 61326, 61362, 61632, 61992, 62136, 62316, 63126, 63162, 63216, 63612, 66132, 66312, 66648, 66864, 68664, 69192, 69912, 72324, 76776, 81312, 81432, 82344, 83112, 83424, 84112, 84312, 84432, 84448, 86664, 88888, 91296, 91692, 91926, 91962, 92196, 92916, 96192, 96912, 99126, 99162, 99216, 99612, 111126, 111162, 111216, 111324, 111432, 111612, 112116, 112266, 112332, 112392, 112626, 112662, 112932, 113124, 113232, 113292, 113322, 113355, 113412, 113535, 113715, 113922, 114132, 114312, 115335, 116112, 116226, 116262, 116622, 119232, 119322, 121116, 121266, 121332, 121392, 121626, 121662, 121932, 122166, 122328, 122364, 122436, 122616, 122664, 122766, 122832, 123132, 123192, 123264, 123312, 123336, 123384, 123624, 123648, 123696, 123864, 123912, 123966, 124236, 124368.

Some larger examples :