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economical n.  and  Proth n.

First numbers that belong to both sets:

3, 5, 13, 17, 25, 41, 49, 81, 97, 113, 129, 145, 161, 177, 193, 241, 257, 289, 353, 449, 577, 641, 673, 769, 929, 961, 1025, 1153, 1217, 1281, 1345, 1409, 1473, 1537, 1601, 1857, 1985, 2049, 2113, 2177, 2241, 2305, 2433, 2625, 2689, 2753, 2881, 3073, 3137, 3265, 3329, 3457, 3521, 3649, 3713, 3969, 4481, 4993, 5761, 6529, 7297, 7681, 7937, 9473, 9601, 9857, 10113, 10369, 10497, 10625, 10753, 11137, 11265, 11393, 11521, 11777, 11905, 12161, 12289, 12417, 12929, 13313, 13441, 13569, 13697, 13825, 13953, 14081, 14337, 14593, 14721, 14849, 14977, 15233, 15361, 15617, 15745, 16001, 16129, 16257, 16641, 16897, 17409, 17665, 17921, 18177, 18433, 19457, 19713, 20225, 20481, 20737, 20993, 21249, 21761, 22273, 23041, 23297, 23809, 24065, 24577, 25089, 25601, 26113, 26369, 26625, 26881, 27649, 27905, 28673, 28929, 29441, 30721, 30977, 31489, 31745, 32257, 33793, 34049, 34817, 35073, 35329, 36097, 36353, 37121, 37633, 37889, 39937, 40193, 40961, 41473, 41729, 42241, 43777, 44801, 45569, 46337, 47105, 47873, 48385, 49409, 49921, 50177, 51457, 51713, 53249, 55553, 57089, 57601, 58369, 58625, 59393, 60161, 61441, 62209, 62977, 64513, 65281, 65537, 66049, 67073, 70657, 76289, 76801, 79873, 80897, 81409, 83969, 84481, 86017, 87041, 87553, 90113, 90625, 95233, 96769, 100865, 101377, 102401, 102913, 103937, 104449, 104961, 105473, 107009, 107521, 108033, 109057, 109569, 110081, 110593, 111105, 112129, 112641, 113153, 114177, 114689, 115201, 116225, 117761, 118273, 118785, 119297, 119809, 120833, 121345, 122369, 123393, 123905, 124417, 124929, 125441, 126465, 127489, 128001, 130049, 130561, 131073, 131585, 132609, 133121, 133633, 134657, 135169, 136193, 137217, 137729, 138241, 138753, 141313, 142849, 143873, 144385, 144897, 145921, 146945, 147457, 148481, 149505, 150017, 151553, 152577, 153089, 153601, 154625, 155137, 156161, 157697, 158209, 159233, 159745, 160257, 161281, 162817, 163329, 163841, 164353, 165377, 165889, 166401.

Some larger examples :