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happy n.  and  Moran n.

First numbers that belong to both sets:

133, 190, 888, 1090, 1141, 1185, 1233, 1251, 1679, 1744, 1812, 1818, 2151, 2313, 2715, 2771, 2919, 3031, 3097, 3123, 3231, 3383, 3546, 4336, 4577, 4842, 4887, 5121, 5274, 5306, 5634, 5817, 6354, 7542, 7859, 8088, 8115, 8397, 8808, 8937, 9012, 9219, 10090, 10727, 10818, 11028, 11085, 11202, 11241, 11358, 11538, 11647, 11805, 11824, 12102, 12108, 12303, 12438, 12762, 13023, 13111, 13518, 13626, 13842, 13881, 14128, 14211, 14562, 14704, 14780, 15021, 15426, 15462, 15519, 16144, 16258, 16326, 16542, 16722, 17461, 18015, 18234, 18342, 18740, 19067, 19171, 19629, 20133, 20151, 20603, 20715, 20752, 20754, 21051, 21102, 21108, 21123, 21213, 21366, 21474, 21501, 21705, 21743, 21834, 22131, 22249, 23013, 23211, 23418, 23454, 23457, 23742, 24191, 24449, 24714, 25072, 25101, 25473, 25614, 25722, 26154, 26221, 26229, 26512, 26575, 26919, 26933, 27015, 27414, 29619, 30123, 30231, 30506, 30546, 30901, 31203, 31221, 31662, 31841, 32013, 32031, 32166, 32272, 32418, 32788, 32814, 33130, 33193, 33310, 34218, 35118, 35575, 36016, 36054, 36304, 36896, 37242, 38032, 39007, 39806, 39912, 40336, 40842, 41274, 41562, 41780, 42111, 42138, 42318, 42357, 42999, 43182, 43506, 44081, 44399, 45054, 45611, 45702, 46959, 47989, 48027, 48402, 48577, 49522, 50121, 50346, 50454, 50742, 51021, 51201, 51318, 51426, 51773, 51807, 52011, 52146, 52294, 53334, 53442, 53571, 53575, 53649, 54342, 54453, 55423, 56142, 56275, 56349, 56725, 57042, 57351, 57990, 58107, 58492, 59790, 59970, 61326, 61709, 62512, 62575, 62669, 62991, 63053, 63789, 63968, 65034, 65214, 65541, 67091, 68337, 68739, 68790, 68937, 70542, 70581, 71596, 72015, 72054, 72126, 72234, 72342, 72456, 73089, 73282, 73422, 73683, 74180, 74322, 74502, 75243, 76122, 76211, 76525, 77247, 77758, 78140, 78639, 78851, 78944, 79267, 80118, 80973, 81105, 81232, 81234, 81342, 81413, 82047, 85071, 86003, 87140, 87876, 87949, 88732, 89073, 90010, 92499, 92691, 93260, 94496.

Some larger examples :