First numbers that belong to both sets:
17,
23,
63,
80,
159,
323,
383,
1023,
2499,
4607,
10239,
15624,
24575,
38879,
52487,
93749,
114687,
177146,
491519,
546874,
705893,
1048575,
1959551,
2228223,
3124999,
4718591,
6377291,
10485759,
13436927,
20726198,
46118407,
46137343,
66961565,
192937983,
363182462,
402653183,
688747535,
872415231.