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Friedman n.  and  semiprime

First numbers that belong to both sets:

25, 121, 289, 1255, 1285, 2501, 2507, 2509, 3281, 4106, 6145, 6455, 10201, 11663, 11665, 12091, 12106, 12769, 12955, 13813, 13822, 13823, 14129, 14647, 15567, 15586, 15613, 15623, 15627, 15634, 15689, 15697, 16295, 16347, 16382, 16387, 16743, 16783, 17482, 19321, 19653, 19693, 21953, 22757, 24385, 25105, 25895, 27889, 29517, 29519, 29549, 29929, 32761, 32762, 32765, 32815, 32845, 32849, 32854, 32855, 32885, 34991, 34993, 35726, 35782, 35942, 37187, 37249, 38427, 39283, 39362, 39363, 43689, 44977, 45363, 45367, 45947, 45957, 46613, 46615, 46637, 46642, 46651, 46653, 46661, 46673, 46677, 48758, 48759, 52483, 52493, 52498, 53297, 54953, 54958, 58973, 59039, 59054, 59057, 59129, 59759, 62503, 64522, 65483, 65489, 65491, 65531, 65542, 67234, 69253, 69985, 74183, 74533, 75433, 77459, 78123, 78133, 83957, 87382, 91853, 97333, 97343, 98305, 98435, 100255, 101299, 102783, 104366, 104897, 104969, 104978, 105295, 106289, 107329, 109351, 109353, 109355, 109358, 112505, 114647, 114697, 116317, 116342, 116635, 116729, 116837, 117067, 117466, 117574, 117578, 117587, 117597, 117613, 117627, 117637, 117641, 117647, 117651, 117653, 117655, 117661, 117662, 117677, 117685, 117695, 117697, 117739, 117767, 117785, 118567, 123199, 123897, 124385, 124483, 124585, 124609, 124851, 124973, 125002, 125007, 125009, 125011, 125014, 125033, 125039, 125041, 125043, 125047, 125051, 125057, 125059, 125061, 125065, 125066, 125071, 125078, 125087, 125089, 125098, 125099, 125317, 125943, 126559, 126563, 126737, 127417, 127454, 128633, 129595, 129603, 129647, 130294, 130679, 131073, 132493, 132497, 132565, 132567, 132653, 132659, 133594, 134455, 134457, 134459, 134462, 134465, 134549, 134689, 134783, 136079, 137257, 137281, 137497, 137539, 137635, 137638, 137642, 137679, 137719, 137729, 137749, 137759, 137779, 137782, 137789, 137794, 137797, 137798, 137859, 137879, 137893, 137899, 138235, 139129, 139677, 142735, 142795, 143857, 144527, 145117, 145273, 146137, 146293, 146337, 146378, 146411, 146413, 146473, 146689, 146758, 147349, 147383, 147439, 147469, 147491, 147493, 147905, 148223, 149782, 151447.

Some larger examples :