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Duffinian n.  and  happy n.

First numbers that belong to both sets:

32, 49, 100, 129, 133, 203, 219, 291, 301, 319, 329, 338, 365, 391, 392, 469, 565, 623, 635, 649, 655, 671, 763, 784, 793, 833, 899, 901, 913, 921, 923, 989, 1003, 1029, 1067, 1115, 1121, 1141, 1177, 1209, 1211, 1247, 1251, 1281, 1285, 1299, 1309, 1333, 1337, 1393, 1411, 1444, 1457, 1533, 1575, 1587, 1679, 1727, 1769, 1771, 1821, 1825, 1841, 1857, 1875, 1903, 1929, 1967, 2019, 2133, 2177, 2181, 2199, 2257, 2285, 2331, 2369, 2425, 2455, 2471, 2485, 2487, 2511, 2527, 2547, 2555, 2575, 2581, 2603, 2717, 2771, 2811, 2815, 2825, 2847, 2881, 2899, 2901, 2989, 2991, 3013, 3065, 3091, 3097, 3103, 3133, 3139, 3153, 3173, 3193, 3233, 3239, 3269, 3283, 3293, 3317, 3351, 3355, 3364, 3365, 3383, 3513, 3535, 3553, 3563, 3605, 3629, 3635, 3653, 3661, 3667, 3689, 3698, 3713, 3763, 3789, 3869, 3897, 3901, 3977, 4009, 4069, 4087, 4096, 4147, 4175, 4181, 4187, 4225, 4255, 4285, 4287, 4356, 4417, 4418, 4449, 4471, 4477, 4525, 4555, 4571, 4577, 4585, 4599, 4609, 4633, 4715, 4741, 4747, 4757, 4775, 4781, 4807, 4811, 4825, 4827, 4841, 4855, 4887, 5063, 5065, 5111, 5211, 5255, 5257, 5275, 5331, 5335, 5353, 5363, 5427, 5455, 5463, 5485, 5517, 5525, 5533, 5555, 5571, 5585, 5603, 5633, 5747, 5789, 5799, 5817, 5855, 5871, 5949, 5965, 5979, 5997, 6017, 6023, 6035, 6049, 6055, 6065, 6083, 6107, 6179, 6239, 6293, 6305, 6307, 6409, 6433, 6463, 6503, 6505, 6533, 6543, 6605, 6613, 6631, 6665, 6789, 6839, 6879, 6893, 6923, 6955, 6989, 7009, 7061, 7063, 7093, 7117, 7133, 7169, 7171, 7217, 7225, 7241, 7255, 7271, 7313, 7363, 7379, 7397, 7415, 7421, 7447, 7475, 7525, 7601, 7619, 7633, 7663, 7711, 7721, 7739, 7744, 7851, 7859, 7869, 7893, 7903, 7959, 7961.

Some larger examples :