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admirable n.  and  balanced n.

First numbers that belong to both sets:

12, 42, 56, 78, 114, 120, 308, 318, 426, 438, 532, 534, 582, 618, 654, 678, 812, 868, 894, 906, 978, 992, 1398, 1758, 1986, 2022, 2154, 2334, 2382, 2406, 2454, 2514, 2586, 2716, 2766, 2778, 3126, 3164, 3250, 3282, 3342, 3378, 3426, 3462, 3522, 3606, 3668, 3724, 3846, 3858, 8415, 8634, 8682, 8826, 8886, 8922, 8934, 9066, 9138, 9186, 9402, 9436, 9555, 9642, 9884, 10398, 10446, 10482, 10554, 10612, 10662, 10698, 10722, 10724, 10806, 10866, 11082, 11096, 11202, 11406, 11442, 11874, 11922, 12066, 12068, 12162, 12522, 12846, 12858, 12908, 12966, 13218, 13638, 13736, 13866, 13972, 14394, 14502, 14538, 14644, 14754, 14862, 15234, 15882, 16256, 17022, 17142, 17274, 17382, 18222, 18402, 18654, 19254, 19914, 19938, 20082, 20166, 21198, 21234, 21426, 24078, 24114, 24798, 25374, 25458, 25554, 26382, 27726, 27858, 28035, 28794, 28902, 28986, 29262, 29514, 29586, 29742, 29838, 29922, 30594, 30918, 31026, 31782, 31818, 32322, 33918, 34014, 34158, 34206, 34266, 34422, 34674, 35166, 35286, 35562, 35756, 35812, 36174, 36438, 36678, 37182, 37302, 37326, 37662, 37722, 38108, 38118, 38202, 38694, 38706, 39126, 39282, 39318, 39378, 39594, 39844, 39966, 40038, 40134, 40146, 40206, 40218, 40292, 41692, 41898, 42078, 42342, 42774, 43242, 43372, 43698, 43876, 44212, 44358, 44706, 45174, 45366, 45462, 45894, 46194, 46362, 46676, 46732, 47274, 47404, 47442, 47778, 49398, 49614, 49638, 49758, 49782, 49974, 50036, 50092, 50118, 50334, 50538, 50574, 50586, 50658, 50766, 50802, 51044, 51078, 51486, 51654, 51882, 52108, 52278, 52314, 52422, 52518, 52556, 52674, 52818, 53072, 53358, 53564, 53646, 53706, 53814, 54042, 54066, 54068, 54572, 54628, 54798, 54822, 55326, 55412, 55446, 55636, 55686, 55698, 55972, 56084, 56346, 56418, 56514, 56586, 56838, 57092, 57678, 57714, 58134, 58182, 58398, 58458, 58722, 58772, 58818, 58902, 59142, 59154, 59948, 60004, 60042, 61518, 61554.

Some larger examples :