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nude n.  and  pandigital

First numbers that belong to both sets:

2, 11, 15, 99, 135, 216, 2226, 13155, 15135, 17955, 31515, 33555, 39195, 39375, 131193, 131931, 153555, 179991, 311535, 319995, 339939, 397971, 513555, 517335, 533115, 575715, 595935, 731535, 733173, 2194164, 2316762, 2323692, 2742712, 2742768, 2743776, 2744112, 2744224, 2784488, 2811872, 2813664, 2817248, 2836344, 2849112, 2873136, 2874648, 2877224, 2877672, 2877784, 2878176, 2973222, 2977632, 3111444, 3111696, 3123624, 3124128, 3136644, 3138912, 3173331, 3227112, 3237864, 3238872, 3242736, 3267768, 3268272, 3271632, 3322326, 3323376, 3336144, 3339315, 3372264, 3373776, 3386712, 3423924, 3434172, 3488184, 3489696, 3612924, 3614688, 3634848, 3647364, 3649716, 3737979, 3786216, 3787728, 3814776, 3817128, 3817296, 3844344, 3848376, 3863832, 3864336, 3922128, 4111632, 4113648, 4113816, 4121824, 4122132, 4122244, 4122272, 4122384, 4138848, 4142124, 4142376, 4143636, 4143888, 4242924, 4324236, 4366236, 4371444, 4373964, 4374132, 4623612, 4624116, 4636128, 4636212, 4636464, 4638648, 4646712, 4647384, 4648728, 4668216, 4668384, 4672248, 4712232, 4712288, 6134184, 6134688, 6167448, 6167784, 6199326, 6211464, 6219864, 6336372, 6646248, 6646332, 6712272, 6714792, 6726132, 6746292, 6749316, 6761412, 6762336, 6772164, 6774432, 6868344, 6868848, 6872376, 6976368, 6978888, 7412664, 7413672, 7431144, 7432824, 7433832, 7511175, 7611324, 7611366, 7646688, 7646772, 7663236, 7663362, 7666722, 7666848, 7742448, 7744632, 7744968, 7818888, 7828128, 7828744, 7837872, 7842184, 7848624, 7848848, 7936488, 7936992, 7961184, 8114848, 8181936, 8182944, 8211336, 8211784, 8217384, 8218728, 8219232, 8269128, 8281224, 8296848, 8316168, 8332128, 8344224, 8731632, 8732136, 8742888, 8743896, 8747928, 8748264, 8779176, 8841168, 8844696, 8862672, 8877288, 8878744, 8968176, 8969688, 9111375, 9131535, 9131976, 9232272, 9233784, 9426312, 9743832, 9748368, 9757755, 9763992, 9777726, 9781128, 9793224, 9826992, 11128712, 11147248, 11221112, 11221448, 11236932, 11264736, 11266248, 11297916, 11322864, 11331768, 11336724, 11336976, 11344368, 11362764, 11366964, 11367216, 11369736, 11474232, 11486328, 11486664, 11488848, 11612622, 11613126, 11613168, 11629296, 11631816, 11633622, 11662224, 11662728, 11736312, 11738832, 11741128, 11744376, 11744712, 11772824, 11777136, 12121116, 12121368, 12121872, 12137412, 12144216, 12174288, 12186384, 12186888, 12187728, 12187784, 12219984, 12293316, 12327126, 12332124, 12334476, 12367236, 12369168, 12371184, 12411672, 12424244, 12426372, 12436368, 12436872, 12444432, 12444768, 12647124.

Some larger examples :