First numbers that belong to both sets:
1105,
8321,
107185,
130561,
2144521,
2181961,
2670361,
8384513,
70484065,
90626185,
297411661,
677451241,
2130804481,
2147418113,
4280622865,
67066235041,
78870812945,
137439477761,
207277205941,
1134757566541,
2199021158401,
8796097216513,
11186038493785,
11238962452961,
444733131907121.