First numbers that belong to both sets:
15,
85,
91,
133,
255,
259,
511,
703,
1111,
1261,
2047,
2071,
2955,
4033,
4369,
4681,
5461,
5551,
6643,
7141,
11155,
16771,
18907,
21845,
25123,
39403,
47989,
53131,
64771,
65535,
65641,
72631,
86731,
99499,
104653,
168421,
198535,
221371,
244531,
291919,
297571,
325471,
335923,
396271,
468541,
576841,
597871,
599845,
737191,
782341,
839515,
875161,
1070191,
1082401,
1377103,
1398101,
1417585,
1438801,
1749007,
1944631,
2016379,
2118481,
2214031,
2497981,
2606611,
3187591,
3188011,
3397651,
3627121,
3788863,
3820909,
4754581,
5310721,
5477941,
5586133,
5864581,
6054061,
6263545,
6277531,
7115557,
8788261,
9305311,
9452551,
9489481,
9925651,
10670023,
11488711,
12326281,
13180531,
13509301,
13881841,
14903461,
15687751,
16843009,
16887991,
17468221,
17518411,
17895697,
19756171,
20380711,
22030681,
22273681,
22369621,
23035201,
27055603,
27883681,
28746559,
29100631,
33554431,
34111441,
36972481,
38124451,
38297533,
39306631,
39419941,
43040161,
44029861,
46710391,
49949557,
50844031,
57146041,
62256349,
64160401,
67905841,
74264821,
79692331,
91327951,
92631001,
99271333,
101412319,
103012351,
104642671,
116715613,
117889591,
121804333,
123754495,
141502921,
149976763,
161285665,
163622473,
164852761,
169767871,
172189309,
175575751,
181454371,
185518471,
191435329,
202233361,
203076751,
203333341,
207950821,
209938015,
216075301,
223367971,
244593961,
245689951,
246066283,
254258971,
254313151,
255242695,
270004099,
286331153,
287932261,
328985791,
339277981,
343490701,
382222051,
387440173,
406889413,
414102151,
422438251,
439554361,
457296841,
458837821,
469177261,
544005169,
564243079,
576168013,
581130733,
599001151,
626275651,
641279653,
703336921,
703602151,
729810901,
744499159,
750239491,
754400011,
768426121,
777545341,
820902889,
847486399,
852871045,
902362819,
921152851,
932722141,
1016940211,
1067296231,
1089363031,
1093788931,
1192140661,
1216928341,
1290569701,
1302091141,
1315549171,
1317735049,
1332943591,
1431655765,
1482844741,
1493088241,
1522198651,
1627355941,
1679811211,
1695833581,
1714415431,
1752217741,
1773026311,
1877445571,
1926375991,
1935988699,
2055670261,
2079182029,
2095762621,
2138380105,
2148354391,
2155234201,
2168395915,
2187479671,
2229267559,
2233082281,
2245385611,
2251929571,
2252499061,
2278677961,
2301711721,
2302032421,
2377098781,
2462198851,
2550763219,
2592795481,
2841165769,
2842542541,
2963223661,
3106223023,
3499846441,
3697510999,
3842843419,
3872359471,
4024697041,
4181626891,
4207070155,
4294967295,
4577053261,
4699856581,
4778419045,
4932323131,
5035250641,
5088610891,
5338421161,
5380842265,
5484957661,
5514473341,
5676793681,
5715435601,
6438317461,
6542701771,
6567400561,
6605870629,
6797814115,
6875643481,
7081576321,
7158767491,
7228485421,
7780915891,
7884561091,
7939255507,
8124643111,
8205551641,
8311513057,
8320180279.
Some larger examples :
799264879681,
807041176411,
813821295289,
814867748941,
840252521389,
846680037061,
852225308761,
859316949043,
860053139491,
862892047921,
869981038999,
884828169601,
893149093531,
911638407649,
937259855239,
947206803271,
949379030965,
964527896281,
970397019901,
984588837961.