First numbers that belong to both sets:
13,
49,
209,
545,
609,
833,
2177,
2369,
2433,
3009,
17153,
52481,
55297,
182273,
195585,
203777,
210945,
300033,
781313,
864257,
1004545,
2621441,
7901185,
8015873,
9101313,
10604545,
17227777,
20406273,
23404545,
35536897,
53067777,
53403649,
55001089,
92504065,
125108225,
170000385,
192430081,
200015873,
267026433,
455606273,
467533825,
622002177,
712015873,
713064449,
887357441,
1045528577,
1071153153,
1224015873,
1484718081.