First numbers that belong to both sets:
3,
5,
13,
17,
97,
193,
257,
577,
769,
1153,
3457,
10369,
12289,
18433,
65537,
147457,
331777,
746497,
786433,
995329,
1179649,
1492993,
1769473,
1990657,
2654209,
5308417,
14155777,
28311553,
63700993,
71663617,
113246209,
169869313,
1811939329,
2717908993,
3221225473,
3439853569,
4076863489,
6879707137,
10871635969,
18345885697,
77309411329,
123834728449,
206158430209,
347892350977,
880602513409.