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nialpdrome  and  Ulam n.

First numbers that belong to both sets:

1, 2, 3, 4, 6, 8, 11, 53, 62, 72, 77, 82, 87, 97, 99, 221, 400, 431, 441, 522, 544, 720, 722, 732, 751, 800, 820, 861, 864, 866, 983, 986, 991, 4211, 5531, 5533, 5550, 6110, 6310, 6322, 6410, 6420, 6520, 6550, 6552, 6633, 6652, 7300, 7322, 7432, 7500, 7520, 7522, 7600, 7622, 7730, 7752, 7754, 7774, 7776, 8421, 8531, 8541, 8553, 8666, 8751, 8754, 8771, 8773, 8842, 8844, 8873, 8876, 9311, 9443, 9511, 9553, 9555, 9621, 9641, 9643, 9663, 9665, 9721, 9743, 9765, 9851, 9853, 9870, 9941, 9961, 9963, 9980, 9983, 9985, 21000, 21110, 31111, 33310, 43311, 44110, 44311, 44411, 52000, 52110, 52210, 53210, 53310, 54111, 54331, 54431, 55321, 55411, 55541, 55543, 55555, 64310, 64420, 65520, 65522, 65542, 65544, 66211, 66443, 66553, 71000, 71110, 72110, 72220, 72222, 73300, 74221, 74433, 75320, 75411, 75430, 75540, 76100, 76210, 76320, 76322, 76430, 76432, 76444, 76554, 77331, 77400, 77441, 77532, 77551, 77554, 77620, 77622, 77661, 77722, 84222, 85221, 85321, 85331, 85522, 85544, 86321, 86431, 86433, 86533, 86541, 86543, 86555, 86621, 86643, 87222, 87310, 87420, 87530, 87665, 88200, 88420, 88422, 88522, 88552, 88554, 88630, 88632, 88654, 88842, 88872, 88874, 92222, 94330, 94440, 95220, 95222, 95432, 95530, 95542, 96322, 96410, 96542, 96544, 96622, 96644, 96661, 96664, 96666, 97211, 97431, 97443, 97531, 97551, 97553, 97666, 97732, 97751, 98220, 98330, 98440, 98611, 98653, 98655, 98741, 98743, 98843, 98873, 98875, 99110, 99220, 99222, 99322, 99430, 99432, 99540, 99542, 99630, 99752, 99755, 99774, 99777, 99843, 99862, 99865, 99911, 99931, 99933, 110000, 111100, 211110, 222000, 222110, 331000, 331110, 420000, 431000, 433111, 443200, 443220, 443222, 444410, 520000, 522221, 532200, 532220, 532222, 533322, 542221, 543110, 543220, 544210, 544422, 552200, 552222, 553111, 554321, 555200, 555222, 555440, 555442, 555530, 555550, 555552, 611111.

Some larger examples :