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happy n.  and  hex n.

First numbers that belong to both sets:

1, 7, 19, 91, 331, 397, 469, 1141, 3367, 4447, 11719, 12481, 14911, 15769, 26227, 27937, 30301, 30907, 33391, 36631, 37297, 39331, 48007, 51877, 56719, 67951, 77281, 85177, 88237, 90307, 96661, 98827, 104347, 106597, 107731, 112327, 113491, 114661, 117019, 119401, 127927, 131671, 140617, 148519, 149857, 151201, 186751, 194311, 195841, 202021, 203581, 221137, 226051, 239419, 254917, 274519, 283669, 287371, 294847, 298621, 323737, 335671, 377011, 381277, 385567, 387721, 394219, 414037, 427519, 429787, 459817, 481201, 493291, 512947, 527941, 548269, 571597, 574219, 576847, 579481, 584767, 587419, 592741, 608851, 655669, 658477, 664111, 669769, 681157, 686887, 701317, 707131, 718831, 742519, 757519, 781831, 797221, 825301, 857071, 873181, 886177, 912457, 925741, 932419, 993601, 1007461, 1010941, 1046071, 1071019, 1143919, 1181269, 1196377, 1211581, 1230721, 1238419, 1250011, 1285111, 1289041, 1308781, 1312747, 1336669, 1368901, 1377019, 1381087, 1389241, 1459519, 1480519, 1488961, 1493191, 1535821, 1548727, 1614067, 1667311, 1703287, 1776391, 1799551, 1804201, 1884169, 1898461, 1927207, 1970731, 2094181, 2114281, 2129419, 2180269, 2268091, 2320561, 2341717, 2357647, 2448937, 2569651, 2619871, 2681911, 2687587, 2744677, 2750419, 2761921, 2767681, 2773447, 2907721, 2949217, 2961127, 3003001, 3009007, 3033091, 3112027, 3161107, 3185791, 3266677, 3431491, 3600361, 3666391, 3746419, 3766561, 3800251, 3847669, 3888547, 3902221, 3950269, 3957157, 3977857, 4103191, 4117237, 4159519, 4259017, 4294837, 4316401, 4374169, 4388671, 4439617, 4454227, 4512907, 4527637, 4564567, 4586797, 4646341, 4698757, 4751467, 4759021, 4857769, 4888357, 4926727, 4949821, 5019427, 5081707, 5160097, 5199517, 5207419, 5247019, 5487769, 5504011, 5552881, 5593771, 5626591, 5651269, 5684257, 5700787, 5709061, 5725627, 5750521, 5783797, 5850637, 5867407, 5960071, 6070519, 6233767, 6566761, 6575641, 6584527, 6682669, 6700591, 6826717, 6862969, 6881131, 6890221, 6944887, 7027291, 7036477, 7054867, 7073281, 7082497, 7091719, 7128667, 7193557, 7258741, 7296121, 7371169, 7579531, 7684801, 7848919, 7858627, 7868341, 7878061, 7985377, 8073721, 8103277, 8311681, 8421901, 8492419, 8603827, 8634337, 8644519, 8654707, 8675101, 8695519, 8726191, 8787697, 8911357, 8942407, 8973511, 9015067, 9025471, 9140311, 9234811, 9414637, 9457201, 9467857, 9489187, 9725401, 9757837, 9866347, 9975457.