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balanced prime  and  hex n.

First numbers that belong to both sets:

22447, 35317, 45757, 73477, 151201, 163567, 329677, 360187, 837937, 879667, 2099197, 2967091, 3310651, 4131307, 4476187, 4972969, 6303151, 8142769, 9067147, 9308647, 11354911, 16237807, 17736577, 22580377, 36008281, 41906719, 42153757, 53184931, 59768497, 64491397, 73344241, 74655397, 91858867, 95479567, 113190919, 118447117, 135011917, 137194219, 156840391, 161869111, 164346607, 166842919, 173987521, 180769219, 190682269, 202828519, 207991807, 214638667, 240817921, 258327361, 263306377, 275933071, 314234971, 320033737, 363297061, 378641971, 396646507, 404271817, 405108061, 429304219, 429806791, 441665467, 445824871, 462582919, 517939381, 528637051, 545333419, 552964057, 568219219, 674865007, 703142371, 718287607, 719216317, 737634241, 738292969, 843950269, 860433481, 861653269, 892842757, 930600469, 933138397, 936845737, 943537471, 948758617, 953887177, 968385367, 976920211, 1058572321, 1066476511, 1068853501, 1068966757, 1108052227, 1158308551, 1181055367, 1217281777, 1238768161, 1271535469, 1284414517, 1309489669, 1309865761, 1360878307, 1371890521, 1380500557, 1437450631, 1464765937, 1543215241, 1599236497, 1623571297, 1679741719, 1786446019, 1795094947, 1873575271, 1896737641, 1904439661, 1919890519, 1979851231, 1991892169, 2005210387, 2009711419, 2042925361, 2102697451, 2258778481, 2382759919, 2410572187, 2417209831, 2509359487, 2617214497, 2694872437, 2759453737, 2837333287, 2849339827, 2920226401, 2940290827, 2957032261, 2998050469, 3003363721, 3033433807, 3084973669, 3167482627, 3186813169, 3265911091, 3312997777, 3340570591, 3438787777, 3546056341, 3550596019, 3583699219, 3692766421, 3753216811, 3754702519, 3882062269, 4018350607, 4045626019, 4061064169, 4103337817, 4173086737, 4251551011, 4286406601, 4326187951, 4430479411, 4479032881, 4599224611, 4715772769, 4733392687, 4764904387, 4838356321, 4855962169, 4910427919, 4932055987, 4983765967, 5122894957, 5170112047, 5202293419, 5314830571, 5344165927, 5454636721, 5494107691, 5543775469, 5577356419, 5628957517, 5704580527, 5765968321, 5965740727, 6007821751, 6046817761, 6096483961, 6248070397, 6268349431, 6431486707, 6566087617, 6578163307, 6644354347, 6648025651, 6742128727, 6762054157, 6784006087, 6831452041, 6843196081, 6968997019, 7162631719, 7262658019, 7291617901, 7374677941, 7411313737, 7421755147, 7464791419, 7540404271, 7586497969, 7630008577, 7657569019, 7680624607, 7687608787, 7883839297, 7887223051, 7909081111, 8018204707, 8133698491, 8144324137, 8222352769, 8232093217, 8272372897, 8320332697, 8379208951, 8510681719, 8512918891, 8577283111, 8593974019, 8674122637, 8687032597, 8689938661, 8726790871, 8981686117, 9057353587, 9142610461, 9332049907, 9567090937, 9633616669, 9746487007, 9820840321, 9854511847, 9974545747.