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Cunningham n.  and  nude n.

First numbers that belong to both sets:

3, 5, 7, 8, 9, 15, 24, 33, 48, 99, 122, 124, 126, 168, 224, 244, 288, 624, 728, 999, 1155, 1224, 1332, 1368, 1848, 1935, 2196, 3126, 3135, 4224, 4488, 5775, 6888, 7224, 7777, 9999, 11448, 12168, 12768, 13224, 16128, 17955, 18224, 24648, 27888, 34224, 42848, 46224, 59535, 71288, 81224, 82368, 94248, 97335, 99999, 111555, 112224, 133224, 134688, 142128, 146688, 148224, 182328, 187488, 214368, 267288, 286224, 332928, 368448, 388128, 413448, 442224, 444888, 466488, 469224, 614124, 616224, 628848, 664224, 683928, 715715, 779688, 822648, 877968, 999999, 1129968, 1138488, 1243224, 1261128, 1283688, 1288224, 1331715, 1338648, 1423248, 1729224, 1841448, 1868688, 1918224, 1923768, 1999395, 2122848, 2146224, 2211168, 2289168, 2362368, 2424248, 2449224, 2666688, 2679768, 2772224, 2778888, 2866248, 3214848, 3323328, 3367224, 3636648, 3736488, 4141224, 4231248, 4264224, 4338888, 4439448, 4464768, 4481688, 4774224, 4897368, 4986288, 6331626, 6436344, 6436368, 6466848, 6682224, 6838224, 6848688, 7991928, 8162448, 8323224, 8614224, 8922168, 9938376, 9999999, 11115555, 11122224, 11323224, 11336688, 11377128, 11444688, 11662224, 11812968, 12439728, 12694968, 12837888, 13126128, 13213224, 13432224, 13446888, 14326224, 14341368, 14386848, 14691888, 15319395, 15555135, 16194276, 16999128, 17355555, 17749368, 18191448, 18361224, 18861648, 18983448, 19123128, 19298448, 19918368, 19936224, 21224448, 21464688, 22231224, 22686168, 23261328, 23668224, 23746128, 23843688, 23863224, 24334488, 24433248, 24631368, 26183688, 26368224, 26388768, 26677224, 26697888, 26863488, 26884224, 27112848, 27426168, 28334328, 28462224, 28761768, 29343888, 31281648, 31618128, 31663128, 32228328, 32341968, 32638368, 33131535, 33466224, 33814224, 34421688, 34633224, 34727448, 35331135, 35593155, 36421224, 36881328, 37613688, 38626224, 41383488, 43467648, 43864128, 44129448, 44422224, 44448888, 44662488, 46144848, 46444224, 46471488, 47817224, 47844888, 48622728, 51351555, 61889688, 62141688, 63313848, 66178224, 66863328, 67782288, 68343288, 68641224, 68674368, 69139224, 69172488, 69438888, 71284248, 72471168, 73393488, 81234168, 81631224, 82319328, 83411688, 84364224, 84916224, 86248368, 86918328, 88228448, 88642224, 88868328, 88981488, 91336248, 91718928, 93412224, 97673688, 98346888, 99999999, 111619224, 111661488, 111999888, 112848128, 113337315, 113784888, 113912928, 114811224, 116488848, 117137328, 117397224, 118222128, 118483224, 118962648, 119399328, 121374288.

Some larger examples :