First numbers that belong to both sets:
3,
5,
7,
17,
37,
257,
577,
1297,
2917,
65537,
147457,
331777,
746497,
5308417,
8503057,
19131877,
6879707137,
347892350977,
1253826625537,
1761205026817,
4518872583697,
5566277615617,
6347497291777,
14281868906497,
39582418599937,
142657607172097.