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happy n.  and  weak prime

First numbers that belong to both sets:

7, 13, 19, 23, 31, 103, 109, 139, 167, 193, 293, 313, 383, 409, 683, 709, 761, 863, 1033, 1039, 1093, 1303, 1373, 1933, 2003, 2039, 2221, 2383, 2393, 2557, 2693, 3001, 3067, 3083, 3137, 3209, 3301, 3323, 3331, 3391, 3463, 3643, 3673, 3709, 3779, 3797, 3803, 3823, 3833, 3923, 3931, 4111, 4363, 4663, 4817, 5281, 5659, 5987, 6053, 6203, 6329, 6343, 6361, 6661, 6703, 6719, 6763, 6803, 6917, 6971, 6983, 7309, 7481, 7541, 7691, 7793, 7937, 8233, 8369, 8693, 8699, 8741, 8821, 9001, 9013, 9203, 9323, 9377, 9623, 10009, 10039, 10093, 10141, 10247, 10303, 10333, 10337, 10487, 10733, 11131, 11243, 11423, 11471, 11491, 11681, 11719, 11941, 11971, 12011, 12101, 12149, 12347, 12413, 12437, 12491, 12671, 12743, 12823, 12853, 12959, 13003, 13009, 13037, 13339, 13421, 13487, 13499, 13577, 13697, 13841, 13903, 13933, 13967, 14011, 14057, 14087, 14207, 14327, 14347, 14437, 14449, 14461, 14537, 14551, 14723, 14783, 14831, 15377, 15451, 15473, 15773, 15823, 16007, 16063, 16363, 16633, 16993, 17033, 17107, 17137, 17191, 17573, 17609, 17627, 17659, 17669, 17713, 17911, 18253, 18401, 18413, 18523, 18587, 18757, 19141, 19333, 19699, 19763, 19963, 19979, 19997, 20177, 20333, 20369, 20393, 20693, 20899, 20903, 20963, 21143, 21149, 21283, 21347, 21407, 21419, 21617, 21841, 22273, 22291, 22483, 22549, 22573, 22621, 22651, 22861, 22921, 23227, 23609, 23899, 24113, 24137, 24181, 24229, 24473, 24683, 24859, 25261, 25801, 25849, 25919, 26003, 26251, 26267, 26633, 26717, 26821, 26903, 27017, 27143, 27283, 27299, 27431, 27617, 27701, 27739, 27793, 27967, 28099, 28123, 28351, 28393, 28411, 28549, 28621, 28771, 28879, 28909, 28933, 29033, 29063, 29303, 29363, 29389, 29411, 29633, 29927, 30013, 30029, 30091, 30139, 30323, 30367, 30391, 30713, 30763, 31039, 31393, 31481, 31547, 31699, 31771, 32009, 32069, 32303, 32309, 32693, 32803, 32887, 33029, 33091.

Some larger examples :