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cyclic n.  and  nialpdrome

First numbers that belong to both sets:

1, 2, 3, 5, 7, 11, 31, 33, 41, 43, 51, 53, 61, 65, 71, 73, 77, 83, 85, 87, 91, 95, 97, 211, 221, 311, 321, 331, 411, 421, 431, 433, 443, 511, 521, 533, 541, 551, 553, 611, 631, 641, 643, 653, 661, 665, 721, 731, 733, 743, 751, 753, 761, 763, 771, 773, 811, 821, 843, 851, 853, 863, 865, 871, 877, 881, 883, 885, 887, 911, 933, 941, 943, 951, 953, 965, 971, 973, 977, 983, 985, 991, 995, 997, 1111, 2111, 2221, 3221, 3331, 3333, 4111, 4211, 4321, 4331, 4333, 4411, 4421, 4433, 4441, 4443, 5111, 5221, 5311, 5321, 5333, 5411, 5431, 5433, 5441, 5443, 5511, 5521, 5531, 5533, 5541, 5543, 5551, 6211, 6221, 6311, 6331, 6333, 6421, 6431, 6433, 6443, 6511, 6521, 6533, 6541, 6551, 6553, 6611, 6621, 6631, 6641, 6643, 6653, 6661, 7211, 7221, 7321, 7331, 7333, 7411, 7421, 7431, 7433, 7441, 7541, 7543, 7553, 7621, 7631, 7633, 7643, 7661, 7663, 7711, 7721, 7733, 7741, 7743, 7751, 7753, 7763, 7765, 7771, 7773, 7777, 8111, 8221, 8311, 8321, 8331, 8333, 8411, 8431, 8441, 8443, 8511, 8521, 8531, 8533, 8543, 8551, 8611, 8621, 8633, 8641, 8651, 8653, 8663, 8665, 8711, 8731, 8733, 8741, 8743, 8753, 8761, 8765, 8773, 8777, 8821, 8831, 8843, 8851, 8861, 8863, 8871, 8873, 8877, 8881, 8885, 8887, 9211, 9221, 9311, 9411, 9421, 9431, 9433, 9511, 9521, 9533, 9551, 9553, 9631, 9643, 9661, 9663, 9665, 9721, 9731, 9733, 9741, 9743, 9753, 9761, 9763, 9771, 9773, 9811, 9821, 9831, 9833, 9841, 9851, 9853, 9863, 9865, 9871, 9877, 9881, 9883, 9885, 9887, 9911, 9931, 9941, 9943, 9953, 9961, 9965, 9973, 9977, 9983, 9985, 9987, 9991, 9995, 9997, 11111, 22111, 22211, 31111, 32111, 32221, 33211.

Some larger examples :