First numbers that belong to both sets:
1,
7,
17,
23,
159,
191,
323,
383,
895,
1023,
1214,
2047,
2499,
4373,
4607,
5119,
10239,
15308,
15624,
24575,
38879,
49151,
52487,
93749,
106495,
114687,
177146,
279935,
491519,
524287,
546874,
590489,
705893,
1048575,
1959551,
2228223,
2359295,
3124999,
4718591,
6377291,
9961471.