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D-number  and  balanced n.

First numbers that belong to both sets:

9, 15, 21, 141, 177, 195, 201, 597, 681, 789, 849, 2103, 2127, 2157, 2199, 2229, 2253, 2319, 2361, 2469, 2481, 2589, 2631, 2643, 2649, 2661, 2757, 2823, 2841, 2913, 2949, 3099, 3117, 3147, 3207, 3273, 3369, 3459, 3489, 3603, 3651, 3777, 3843, 3849, 3873, 7017, 7041, 7179, 7197, 7251, 7827, 7851, 7971, 8223, 8247, 8331, 8367, 8403, 8457, 8553, 8571, 8661, 8751, 8859, 8871, 8889, 8907, 9003, 9069, 9123, 9411, 9501, 9543, 9561, 9573, 9663, 9771, 9813, 9897, 9987, 10299, 10347, 10383, 10389, 10401, 10407, 10473, 10581, 10617, 10713, 10749, 10779, 10851, 10893, 10929, 10977, 11019, 11091, 11283, 11307, 11463, 11469, 11541, 11559, 11589, 11733, 11769, 11787, 11841, 11967, 12171, 12237, 12381, 12459, 12531, 12633, 12651, 12657, 12693, 12723, 12891, 13341, 13389, 13521, 13569, 13641, 13701, 13809, 14163, 14169, 14199, 14277, 14379, 14403, 14439, 14451, 14613, 14709, 14727, 14871, 14919, 14961, 14979, 14997, 15009, 15177, 15441, 15459, 15513, 15537, 15627, 15681, 15693, 15837, 15843, 15891, 15909, 15969, 16143, 16179, 16221, 16257, 16449, 16557, 16581, 16689, 16695, 16869, 16941, 16959, 17007, 17067, 17079, 17133, 17337, 17583, 17643, 17781, 18021, 18219, 18267, 18273, 18339, 18363, 18399, 18489, 18591, 18633, 18651, 18663, 18741, 18831, 18915, 19059, 19281, 19347, 19563, 19641, 19689, 20067, 20103, 20109, 21039, 21171, 21387, 22587, 22731, 24699, 24807, 24879, 24891, 25059, 25167, 25287, 25293, 25329, 25383, 25401, 25743, 25827, 26679, 26823, 27399, 27411, 27723, 27849, 28173, 28209, 28839, 28857, 29067, 29091, 29229, 29361, 29409, 29577, 30759, 30777, 30819, 30867, 31011, 31107, 31281, 31299, 31497, 31881, 33207, 33213, 33261, 33591, 33639, 33717, 33753, 33951, 34107, 34233, 34413, 34509, 34737, 34761, 35031, 35103, 35151, 35193, 35229, 35421, 35499, 35661, 35781, 35943, 35961, 36021, 36111, 36123, 36147, 36291, 36321, 36429, 36633, 36681.

Some larger examples :