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happy n.  and  plaindrome

First numbers that belong to both sets:

1, 7, 13, 19, 23, 28, 44, 49, 68, 79, 129, 133, 139, 167, 188, 226, 236, 239, 338, 356, 367, 368, 379, 446, 469, 478, 556, 566, 888, 899, 1112, 1114, 1115, 1122, 1125, 1128, 1148, 1158, 1177, 1188, 1222, 1233, 1247, 1257, 1258, 1277, 1288, 1299, 1333, 1335, 1337, 1339, 1366, 1444, 1447, 1448, 1457, 1478, 1557, 1578, 1599, 1666, 1679, 1888, 2224, 2245, 2257, 2258, 2333, 2338, 2339, 2369, 2448, 2455, 2457, 2458, 2478, 2555, 2557, 2568, 2899, 3338, 3346, 3355, 3356, 3367, 3456, 3466, 3667, 3689, 3779, 3789, 4447, 4449, 4455, 4477, 4555, 4558, 4577, 4599, 4788, 4888, 5555, 5558, 5569, 5666, 5789, 5799, 6789, 6899, 7788, 11113, 11118, 11124, 11125, 11134, 11145, 11147, 11149, 11159, 11168, 11179, 11223, 11229, 11234, 11238, 11248, 11249, 11267, 11348, 11358, 11377, 11388, 11446, 11455, 11456, 11467, 11559, 12226, 12229, 12238, 12256, 12267, 12268, 12279, 12333, 12347, 12348, 12358, 12366, 12399, 12447, 12456, 12556, 12568, 12599, 12677, 12699, 12778, 13334, 13339, 13366, 13447, 13457, 13478, 13499, 13557, 13577, 13679, 13699, 13889, 13899, 14449, 14456, 14459, 14468, 14556, 14889, 15679, 15688, 15778, 15788, 16669, 16679, 16899, 16999, 17999, 18899, 22224, 22229, 22237, 22244, 22249, 22257, 22267, 22269, 22344, 22347, 22348, 22357, 22378, 22459, 22467, 22556, 22559, 22568, 22667, 22799, 23366, 23369, 23389, 23445, 23447, 23448, 23455, 23457, 23468, 23779, 23788, 23899, 24444, 24449, 24455, 24456, 24567, 24589, 24777, 24999, 25567, 25578, 25688, 25777, 25779, 26668, 26669, 26779, 27788, 27889, 33338, 33345, 33346, 33359, 33446, 33589, 33667, 33678, 34445, 34455, 34458, 34477, 34499, 34555, 34558, 34569, 34666, 34789, 34799, 35555, 35557, 35569, 35888, 36689, 36777, 36789, 37999, 44446, 44456, 44467, 44488, 44489, 44566, 44599, 44699, 44789, 45678, 45699, 45777, 45778, 46668, 46799.

Some larger examples :