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junction n.  and  nude n.

First numbers that belong to both sets:

111, 115, 212, 216, 315, 412, 515, 612, 816, 824, 1112, 1116, 1722, 1926, 2212, 2412, 2616, 2622, 2824, 3312, 3924, 4212, 4412, 4416, 4424, 4824, 6216, 6222, 6612, 6624, 6816, 7112, 7728, 8224, 8424, 8616, 8824, 8832, 9126, 9324, 11111, 11115, 11212, 11313, 11412, 11515, 11616, 11622, 11711, 11824, 12112, 12312, 12712, 12726, 12924, 13113, 13212, 13311, 13416, 13515, 13626, 13713, 13824, 14112, 14316, 14728, 15115, 15315, 15515, 15715, 16116, 16122, 16326, 16716, 17115, 17717, 18112, 18312, 19224, 19719, 19935, 21112, 21312, 21924, 22212, 22222, 22412, 22416, 22424, 22626, 22824, 23112, 23316, 23322, 23922, 24212, 24216, 24224, 24412, 24424, 24612, 24624, 24816, 24824, 26226, 26412, 26424, 26616, 26622, 26832, 28224, 28416, 28424, 28632, 28824, 29124, 29322, 31113, 31212, 31311, 31416, 31515, 31626, 31824, 32112, 32316, 32322, 32922, 33111, 33117, 33216, 33222, 33315, 33612, 33624, 33816, 34116, 35115, 36126, 36312, 36324, 37212, 37317, 37632, 38112, 38328, 39222, 39933, 41112, 41316, 42212, 42216, 42224, 42412, 42424, 42612, 42624, 42816, 42824, 43116, 44212, 44224, 44412, 44424, 44616, 44824, 44832, 46212, 46224, 46416, 46632, 46824, 47124, 48216, 48224, 48424, 48432, 48624, 48824, 49932, 51115, 51315, 51515, 53115, 55115, 55515, 55935, 59535, 61116, 61122, 61326, 62226, 62412, 62424, 62616, 62622, 62832, 63126, 63312, 63324, 64212, 64224, 64416, 64632, 64824, 66216, 66222, 66432, 66624, 67116, 67326, 68232, 68424, 68832, 71715, 72324, 73416, 73626, 73731, 77224, 77931, 79632, 81112, 81312, 82224, 82416, 82424, 82632, 82824, 83112, 83328, 84216, 84224, 84424, 84432, 84624, 84824, 86232, 86424, 86832, 88224, 88424, 88632, 88824, 89928, 91224, 91935, 92124, 92322, 93222, 93933, 94932, 95535, 97335, 98928, 99135, 99333, 99432, 111112, 111312, 111924, 112212, 112222, 112412, 112416, 112424, 112626, 112824, 113112, 113316, 113322, 113922, 114212, 114216, 114224, 114412, 114424, 114612, 114624, 114816.

Some larger examples :