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happy n.  and  tau n.

First numbers that belong to both sets:

1, 376, 536, 632, 904, 1112, 1152, 1212, 1332, 1448, 1521, 1528, 1572, 1784, 1812, 1920, 2008, 2748, 2784, 2844, 2936, 3456, 3736, 3760, 3832, 3896, 3968, 4184, 4248, 4284, 4552, 4572, 4744, 4788, 4824, 5112, 5128, 5172, 5224, 5248, 5268, 5272, 5360, 5364, 5436, 5472, 5752, 5824, 6008, 6056, 6320, 6376, 6528, 6616, 6852, 6904, 7016, 7048, 7284, 7428, 7524, 7552, 7848, 7968, 8152, 8244, 8488, 8512, 8724, 8796, 8880, 8936, 9012, 9032, 9040, 9120, 9368, 9444, 9876, 9896, 10000, 10112, 10188, 10332, 10572, 10880, 10888, 11028, 11048, 11052, 11120, 11232, 11250, 11280, 11292, 11384, 11412, 11432, 11464, 11512, 11672, 11808, 12088, 12108, 12132, 12184, 12192, 12276, 12321, 12348, 12384, 12456, 12564, 12568, 12636, 12672, 12776, 12808, 12856, 12880, 13032, 13122, 13184, 13212, 13428, 13784, 13812, 13976, 14072, 14312, 14328, 14408, 14480, 14556, 14648, 14652, 14720, 14724, 14988, 15072, 15108, 15112, 15120, 15138, 15208, 15256, 15264, 15280, 15456, 15464, 15564, 15832, 15944, 15976, 15992, 16236, 16452, 16524, 16552, 16696, 16712, 16992, 17024, 17048, 17096, 17244, 17432, 17508, 17520, 17840, 18008, 18108, 18132, 18180, 18324, 18432, 18808, 18856, 18948, 18996, 19212, 19296, 19488, 19576, 19692, 19736, 19760, 19884, 19920, 20080, 20448, 20484, 20936, 21108, 21120, 21132, 21176, 21256, 21348, 21564, 21636, 21704, 21792, 21832, 21972, 21996, 22024, 22176, 22216, 22424, 22476, 22716, 22752, 22856, 22912, 23096, 23148, 23272, 23424, 23724, 23744, 23752, 23844, 23936, 24156, 24324, 24328, 24348, 24372, 24444, 24480, 24672, 24756, 24804, 24952, 25068, 25216, 25416, 25644, 25680, 25840, 25984, 26172, 26316, 26552, 27252, 27264, 27328, 27520, 27540, 27564, 27612, 27992, 28044, 28216, 28312, 28560, 28568, 28704, 28856, 29196, 29360, 30132, 30312, 30376, 30664, 31032, 31212, 31284, 32128, 32148, 32244, 32484, 32544, 32728, 32744, 33012, 33032, 33064, 33120.

Some larger examples :