First numbers that belong to both sets:
3,
5,
9,
13,
17,
25,
33,
49,
57,
113,
129,
145,
177,
225,
257,
289,
449,
577,
1345,
2369,
2689,
3457,
3777,
5889,
11137,
11777,
12289,
13569,
24577,
37889,
45569,
114689,
122369,
677889,
1355777,
1445889,
11112449,
14667777,
22347777,
23666689,
222445569,
223346689,
1124466689.