First numbers that belong to both sets:
3,
5,
17,
163,
257,
1297,
2593,
10369,
17497,
65537,
139969,
331777,
472393,
2654209,
5308417,
11337409,
57395629,
71663617,
86093443,
102036673,
120932353,
169869313,
483729409,
725594113.