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nialpdrome  and  semiprime

First numbers that belong to both sets:

4, 6, 9, 10, 21, 22, 33, 51, 55, 62, 65, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 111, 221, 321, 411, 422, 511, 533, 542, 543, 551, 553, 554, 611, 622, 633, 655, 662, 721, 731, 753, 755, 763, 766, 771, 831, 841, 842, 843, 851, 862, 865, 866, 871, 886, 921, 922, 933, 943, 951, 955, 961, 965, 973, 974, 982, 985, 993, 995, 998, 1111, 4222, 4321, 4322, 4331, 4333, 4411, 4442, 4443, 5111, 5221, 5311, 5321, 5331, 5411, 5422, 5433, 5533, 5541, 5543, 5554, 6331, 6333, 6411, 6431, 6433, 6442, 6443, 6511, 6533, 6541, 6542, 6611, 6621, 6631, 6641, 6662, 6663, 7111, 7311, 7421, 7431, 7441, 7522, 7531, 7543, 7555, 7631, 7633, 7642, 7651, 7653, 7655, 7661, 7663, 7666, 7711, 7721, 7751, 7754, 7762, 7763, 7765, 7771, 7773, 8222, 8321, 8331, 8333, 8411, 8422, 8441, 8511, 8522, 8531, 8542, 8551, 8553, 8611, 8621, 8633, 8651, 8653, 8654, 8661, 8665, 8711, 8743, 8751, 8765, 8773, 8777, 8842, 8843, 8851, 8871, 8873, 8881, 8882, 8885, 9111, 9211, 9411, 9442, 9543, 9553, 9611, 9641, 9651, 9655, 9662, 9663, 9665, 9722, 9731, 9742, 9753, 9754, 9755, 9761, 9763, 9771, 9773, 9777, 9841, 9853, 9862, 9863, 9865, 9866, 9874, 9881, 9886, 9921, 9943, 9953, 9961, 9965, 9974, 9977, 9983, 9985, 9986, 9987, 9991, 9993, 9995, 9997, 9998, 11111, 31111, 32111, 32221, 32222, 33221, 33322, 43111, 43211, 43221, 43222, 43311, 43322, 43333, 44211, 44222, 44311, 44333, 44411, 44431, 44441, 52211, 52222, 53111, 53211, 53221, 53311, 53321, 54211, 54221, 54422, 54433, 55111, 55222, 55421, 55433, 55443, 55531, 55543, 55551, 55553, 61111, 62221, 63221, 63321, 64111, 64211, 64221, 64321, 64331, 64411, 64421, 64441, 64443, 65211, 65222, 65311, 65321, 65333, 65411, 65431.

Some larger examples :