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happy n.  and  self n.

First numbers that belong to both sets:

1, 7, 31, 86, 97, 176, 310, 356, 367, 446, 490, 536, 637, 716, 793, 940, 973, 1076, 1122, 1177, 1188, 1212, 1300, 1335, 1390, 1447, 1581, 1717, 1772, 1818, 1851, 1930, 2112, 2211, 2224, 2257, 2369, 2448, 2527, 2571, 2582, 2639, 2751, 2784, 2852, 2874, 3056, 3067, 3100, 3135, 3190, 3269, 3313, 3315, 3392, 3605, 3616, 3629, 3673, 3706, 3763, 3897, 3932, 3987, 4009, 4046, 4090, 4147, 4248, 4417, 4428, 4494, 4663, 4718, 4775, 4887, 4944, 5036, 5181, 5227, 5271, 5282, 5506, 5517, 5552, 5585, 5596, 5721, 5798, 5822, 5855, 5956, 5978, 6037, 6239, 6305, 6316, 6329, 6373, 6463, 6643, 6665, 6733, 7093, 7117, 7172, 7251, 7284, 7306, 7363, 7418, 7475, 7521, 7598, 7633, 7721, 7745, 7824, 7958, 8002, 8118, 8151, 8252, 8274, 8397, 8487, 8522, 8555, 8724, 8801, 8812, 8847, 8880, 8937, 8992, 9040, 9073, 9130, 9332, 9387, 9444, 9556, 9578, 9758, 9837, 9892, 9982, 10076, 10122, 10177, 10188, 10212, 10300, 10335, 10390, 10447, 10581, 10717, 10772, 10818, 10851, 10930, 11022, 11077, 11088, 11134, 11145, 11314, 11358, 11413, 11415, 11492, 11514, 11538, 11672, 11762, 11773, 11942, 12201, 12291, 12348, 12381, 12438, 12583, 12831, 12853, 12921, 13009, 13035, 13090, 13114, 13158, 13248, 13281, 13303, 13393, 13428, 13472, 13518, 13606, 13663, 13742, 13775, 13821, 13898, 13933, 13988, 14047, 14113, 14115, 14192, 14238, 14328, 14372, 14416, 14440, 14473, 14495, 14708, 14732, 14743, 14921, 14945, 15011, 15081, 15114, 15138, 15283, 15318, 15507, 15564, 15654, 15720, 15788, 15810, 15823, 15878, 15911, 15990, 16172, 16306, 16363, 16554, 16633, 16721, 16811, 16822, 17072, 17162, 17173, 17342, 17375, 17408, 17432, 17443, 17520, 17588, 17621, 17735, 17858, 18014, 18051, 18231, 18253, 18321, 18398, 18510, 18523, 18578, 18611, 18622, 18758, 18802, 18813, 18938, 18993, 19030, 19142, 19221, 19333.

Some larger examples :