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brilliant n.  and  nialpdrome

First numbers that belong to both sets:

4, 6, 9, 10, 21, 221, 533, 551, 611, 731, 841, 851, 871, 943, 961, 4331, 7663, 8633, 32111, 33221, 44431, 52211, 53111, 55421, 63221, 64321, 65311, 65411, 66331, 66421, 66511, 66641, 73111, 73211, 75311, 75421, 75433, 76621, 76633, 77321, 77411, 82111, 82211, 83333, 85511, 85541, 85543, 86221, 88433, 88531, 88631, 88831, 88871, 91111, 95321, 96511, 96521, 96641, 97333, 97541, 97663, 97751, 98333, 98431, 98551, 98741, 98863, 99221, 99443, 99511, 99553, 99653, 99811, 99821, 99941, 99973, 222221, 322211, 431111, 544421, 554441, 664333, 755221, 774443, 5443331, 5555531, 5555533, 6331111, 6433321, 6532111, 6533333, 6544331, 6554111, 6555331, 6555511, 6632111, 6644333, 6653333, 6654421, 6665221, 6665441, 6665443, 6665521, 6666221, 6666553, 7333111, 7444211, 7542211, 7554221, 7622221, 7631111, 7633331, 7654421, 7654433, 7655441, 7655551, 7664441, 7664443, 7665331, 7665551, 7666111, 7666441, 7744111, 7753331, 7755221, 7755431, 7755541, 7763321, 7766333, 7773221, 7774111, 8333321, 8333333, 8444321, 8444441, 8533331, 8543221, 8554411, 8554433, 8643221, 8655511, 8655553, 8664211, 8665331, 8666551, 8666663, 8711111, 8742211, 8744221, 8753333, 8754211, 8763221, 8765311, 8765443, 8765531, 8774411, 8775421, 8775433, 8776333, 8776433, 8776661, 8777653, 8777761, 8777777, 8832221, 8842111, 8843321, 8852111, 8855443, 8863111, 8864441, 8865221, 8873311, 8875553, 8876333, 8876521, 8877641, 8877721, 8883331, 8884111, 8884333, 8884441, 8885431, 8886221, 8886643, 8887771, 8888533, 8888543, 8888777, 8888863, 9332221, 9432211, 9443111, 9443221, 9541111, 9543221, 9544421, 9554411, 9622111, 9644311, 9644431, 9653321, 9654431, 9663211, 9663221, 9664111, 9665111, 9666211, 9666221, 9666641, 9744221, 9744311, 9754331, 9755311, 9755533, 9763333, 9765541, 9766111, 9766441, 9766663, 9773111, 9774431, 9775333, 9775411, 9777433, 9777743, 9833321, 9843331, 9844333, 9844421, 9844441, 9853331, 9854111, 9863333, 9865111, 9866543, 9875531, 9876311, 9876431, 9876551, 9877771, 9884111, 9884333, 9885431, 9886663, 9888811, 9888821, 9942221, 9943321, 9944411, 9963221, 9966311, 9966631, 9966661, 9974311, 9975443, 9976441, 9976543, 9976663, 9977441, 9977761, 9984433, 9985411, 9985531, 9987751, 9988421, 9988763, 9988883, 9995543, 9996331, 9996521, 9996533, 9996611, 9996643, 9997633, 9997763, 9998311, 9998411, 9998531, 9998773.

Some larger examples :