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happy n.  and  untouchable n.

First numbers that belong to both sets:

188, 262, 326, 556, 748, 784, 802, 818, 836, 964, 1128, 1148, 1212, 1222, 1258, 1288, 1332, 1418, 1528, 1578, 1758, 1844, 1852, 1888, 1920, 1992, 2008, 2036, 2062, 2118, 2158, 2174, 2190, 2212, 2258, 2306, 2338, 2422, 2452, 2484, 2518, 2568, 2572, 2586, 2602, 2748, 2784, 2856, 2874, 3076, 3132, 3238, 3296, 3312, 3328, 3356, 3506, 3564, 3650, 3670, 3760, 3832, 3860, 3902, 3986, 4046, 4078, 4148, 4172, 4184, 4248, 4258, 4336, 4356, 4406, 4690, 4712, 4718, 4782, 4842, 5178, 5218, 5224, 5286, 5346, 5360, 5364, 5428, 5458, 5542, 5544, 5552, 5596, 5606, 5666, 5722, 5724, 5798, 6308, 6350, 6528, 6800, 6852, 6904, 7142, 7144, 7158, 7172, 7360, 7366, 7428, 7444, 7512, 7522, 7598, 7788, 7840, 7848, 7900, 7916, 8006, 8036, 8108, 8152, 8218, 8360, 8442, 8478, 8488, 8512, 8562, 8704, 8724, 8778, 8812, 8818, 8848, 8874, 8990, 8992, 9098, 9120, 9192, 9236, 9298, 9302, 9332, 9362, 9368, 9444, 9556, 9578, 9638, 9716, 9758, 9786, 9876, 9896, 9980, 9982, 10076, 10148, 10158, 10222, 10258, 10300, 10366, 10448, 10472, 10484, 10512, 10528, 10578, 10582, 10636, 10748, 10752, 10758, 10812, 10814, 10880, 10888, 10902, 10920, 10930, 11014, 11082, 11102, 11154, 11168, 11186, 11202, 11220, 11232, 11234, 11248, 11342, 11358, 11382, 11408, 11428, 11432, 11456, 11464, 11480, 11502, 11510, 11512, 11564, 11672, 11714, 11726, 11820, 11838, 11880, 12132, 12134, 12210, 12220, 12238, 12276, 12318, 12358, 12418, 12456, 12470, 12508, 12562, 12568, 12636, 12762, 12808, 12850, 12862, 12880, 12990, 13000, 13030, 13090, 13142, 13182, 13212, 13228, 13248, 13258, 13266, 13284, 13302, 13320, 13350, 13428, 13474, 13530, 13582, 13662, 13742, 13744, 13812, 13814, 13818, 13824, 13900, 13976, 13992, 14018, 14048, 14078, 14128, 14132, 14164, 14192, 14312, 14318, 14468, 14472, 14486, 14516, 14526, 14570, 14810.

Some larger examples :