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cyclic n.  and  super-d n.

First numbers that belong to both sets:

19, 31, 69, 107, 119, 127, 131, 181, 247, 269, 281, 319, 331, 335, 337, 339, 419, 431, 469, 481, 511, 519, 569, 581, 601, 619, 631, 679, 681, 719, 731, 739, 749, 753, 769, 781, 869, 881, 919, 1019, 1031, 1049, 1051, 1057, 1059, 1061, 1063, 1067, 1069, 1123, 1145, 1169, 1181, 1219, 1231, 1319, 1381, 1453, 1469, 1471, 1481, 1487, 1531, 1619, 1631, 1645, 1669, 1761, 1769, 1781, 1819, 1831, 1847, 1901, 1919, 1923, 1931, 1969, 1981, 2031, 2069, 2081, 2119, 2131, 2159, 2219, 2231, 2261, 2269, 2281, 2319, 2363, 2369, 2381, 2395, 2419, 2431, 2471, 2473, 2477, 2479, 2481, 2519, 2531, 2569, 2571, 2581, 2591, 2627, 2669, 2681, 2719, 2731, 2759, 2819, 2831, 2869, 2881, 2931, 2935, 2969, 2981, 3011, 3019, 3031, 3035, 3119, 3131, 3163, 3169, 3181, 3239, 3269, 3281, 3317, 3319, 3323, 3327, 3329, 3331, 3333, 3335, 3337, 3341, 3343, 3347, 3349, 3353, 3359, 3361, 3365, 3367, 3371, 3373, 3377, 3379, 3383, 3385, 3389, 3391, 3419, 3431, 3469, 3531, 3569, 3581, 3619, 3621, 3623, 3631, 3669, 3719, 3731, 3769, 3781, 3831, 3851, 3855, 3869, 3877, 3881, 3919, 3931, 4013, 4019, 4031, 4081, 4119, 4169, 4181, 4219, 4231, 4261, 4281, 4285, 4331, 4369, 4381, 4451, 4469, 4471, 4479, 4481, 4519, 4531, 4569, 4595, 4597, 4611, 4619, 4631, 4649, 4681, 4755, 4769, 4781, 4819, 4831, 4873, 4919, 4931, 4969, 4981, 5011, 5069, 5081, 5111, 5113, 5119, 5127, 5131, 5207, 5231, 5269, 5281, 5369, 5381, 5419, 5431, 5469, 5471, 5501, 5511, 5519, 5531, 5533, 5569, 5579, 5581, 5623, 5631, 5645, 5667, 5669, 5681, 5731, 5739, 5781, 5869, 5881, 5919, 5969, 5981, 6009, 6011, 6019, 6031, 6059, 6081, 6119, 6131, 6133, 6145, 6169, 6269, 6281, 6319, 6331, 6431, 6469.

Some larger examples :