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equidigital n.  and  happy n.

First numbers that belong to both sets:

1, 7, 10, 13, 19, 23, 31, 32, 49, 79, 97, 103, 109, 129, 133, 139, 167, 192, 193, 203, 219, 239, 263, 291, 293, 301, 313, 320, 329, 331, 365, 367, 379, 383, 397, 409, 469, 487, 563, 617, 623, 653, 673, 683, 709, 739, 761, 863, 881, 907, 937, 1000, 1003, 1009, 1033, 1039, 1067, 1088, 1093, 1114, 1115, 1121, 1125, 1141, 1151, 1152, 1184, 1185, 1211, 1247, 1257, 1277, 1281, 1285, 1299, 1303, 1323, 1333, 1335, 1337, 1366, 1373, 1393, 1411, 1418, 1427, 1447, 1457, 1472, 1475, 1478, 1481, 1487, 1511, 1527, 1533, 1574, 1587, 1607, 1663, 1679, 1697, 1706, 1733, 1745, 1754, 1769, 1814, 1821, 1825, 1841, 1847, 1851, 1857, 1874, 1882, 1888, 1920, 1929, 1933, 1959, 1967, 2003, 2019, 2039, 2063, 2111, 2133, 2157, 2177, 2181, 2199, 2221, 2245, 2257, 2285, 2309, 2333, 2339, 2383, 2393, 2417, 2425, 2455, 2471, 2485, 2487, 2511, 2517, 2527, 2528, 2545, 2555, 2557, 2571, 2581, 2693, 2741, 2752, 2811, 2815, 2833, 2845, 2851, 2881, 2901, 2903, 2933, 2963, 2989, 2991, 3001, 3019, 3031, 3065, 3067, 3079, 3083, 3109, 3137, 3139, 3200, 3209, 3233, 3239, 3269, 3283, 3293, 3301, 3313, 3319, 3321, 3323, 3328, 3329, 3331, 3365, 3371, 3391, 3392, 3456, 3463, 3563, 3607, 3635, 3637, 3643, 3661, 3673, 3698, 3709, 3713, 3763, 3779, 3797, 3803, 3823, 3833, 3869, 3901, 3907, 3923, 3931, 3968, 3977, 4087, 4111, 4127, 4157, 4187, 4217, 4271, 4285, 4363, 4417, 4418, 4441, 4447, 4481, 4517, 4555, 4571, 4663, 4721, 4751, 4757, 4781, 4817, 4855, 4871, 5056, 5063, 5147, 5227, 5248, 5257, 5281, 5417, 5427, 5471, 5477, 5527, 5569, 5659, 5741, 5747, 5751, 5789, 5821, 5879, 5897, 5987, 6037, 6053, 6073, 6163, 6197, 6203, 6329, 6337.

Some larger examples :