First numbers that belong to both sets:
5,
17,
41,
97,
257,
641,
929,
3457,
4481,
11777,
61441,
65537,
168449,
878593,
1210369,
1374209,
1417217,
1652737,
1689601,
3604481,
4005889,
5578753,
6086657,
11038721,
12361729,
12599297,
18210817,
29286401,
29483009,
49471489,
79003649,
84213761,
102793217,
167723009,
190857217.