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happy n.  and  Sophie Germain prime

First numbers that belong to both sets:

23, 239, 293, 653, 683, 761, 1481, 1511, 1733, 2003, 2039, 2063, 2339, 2393, 2693, 2741, 2903, 2963, 3329, 3779, 3803, 4271, 4481, 4871, 5741, 6053, 6329, 6899, 6983, 7541, 7691, 7841, 8693, 8741, 8969, 9689, 10733, 11471, 11519, 12011, 12101, 12671, 12959, 14081, 14321, 14561, 14783, 14831, 14939, 15101, 15773, 16811, 17669, 18041, 18341, 18899, 19889, 20063, 20369, 20393, 20693, 20771, 20963, 21011, 21149, 21341, 21419, 24473, 24683, 25919, 26633, 27143, 28643, 29033, 29363, 30269, 30323, 30689, 32009, 32141, 33023, 34949, 35933, 36791, 36923, 37013, 37619, 38189, 38303, 38333, 38669, 38891, 39419, 41081, 41231, 41381, 41399, 42071, 42131, 42473, 42743, 43313, 43721, 44249, 44273, 44543, 44651, 44699, 44879, 45641, 47501, 47513, 48131, 48479, 48731, 49193, 50741, 54443, 54941, 55229, 57041, 57413, 57881, 60083, 60293, 60719, 62171, 63179, 64451, 66791, 67121, 67169, 67499, 68111, 68639, 68963, 69203, 69809, 70061, 70313, 70379, 70589, 70793, 71453, 71693, 71843, 71999, 72161, 73421, 73709, 73751, 74201, 74381, 74699, 75041, 76001, 76091, 77261, 77513, 78059, 78341, 78509, 79349, 79613, 80369, 81611, 81839, 84011, 84131, 84263, 84401, 84449, 84713, 86111, 86441, 88919, 90089, 91529, 92003, 92363, 92951, 93479, 93941, 96731, 97943, 98981, 99251, 101429, 101483, 101681, 102149, 104183, 104231, 104399, 104561, 105929, 106451, 107843, 108401, 109883, 111509, 111959, 113783, 114269, 115001, 115553, 115679, 116579, 116969, 117041, 117779, 118043, 118259, 118589, 120671, 120941, 121139, 121403, 121763, 121931, 122231, 123401, 124643, 126443, 126491, 126713, 127973, 128951, 129401, 129509, 129581, 130241, 131441, 131783, 133571, 133979, 134591, 135221, 135329, 135731, 137993, 137999, 138041, 139409, 139739, 140813, 140831, 141413, 141539, 141803, 144563, 145643, 145679, 146543, 147011, 147083, 147503, 148013, 148331, 148829, 149021, 149153, 149531, 150011, 150743, 151289, 151769, 151901, 152819, 154769, 156041, 157133, 157271, 158129, 158981, 159209, 159233, 159431, 159671, 161561.

Some larger examples :