First numbers that belong to both sets:
3,
5,
7,
10,
15,
17,
31,
35,
37,
101,
122,
127,
129,
145,
197,
215,
217,
224,
257,
401,
485,
511,
577,
677,
1025,
1088,
1157,
1226,
1295,
1297,
1445,
1522,
1601,
1682,
1763,
1765,
2047,
2049,
2117,
2303,
2305,
2501,
2705,
2917,
3137,
3365,
3599,
3845,
3968,
4357,
4625,
5183,
5477,
5831,
6399,
6723,
7057,
8101,
8191,
8837,
10001,
10202,
10405,
10649,
10817,
11237,
11665,
12101,
12997,
13457,
13690,
13823,
13825,
13925,
14162,
14401,
14642,
15375,
15377,
15875,
15877,
16128,
16640,
16901,
17162,
17577,
17957,
18497,
19322,
19882,
20737,
21317,
21951,
21953,
22501,
23105,
23717,
24337,
24965,
25280,
25601,
25920,
28901,
29585,
30977,
31685,
32401,
33857,
35345,
37248,
37637,
38417,
39205,
40805,
41617,
42437,
44101,
49285,
50177,
52901,
55697,
57601,
58563,
59535,
60517,
62501,
65024,
65537,
66048,
67601,
69697,
72901,
78401,
80657,
90001,
93637,
98597,
100001,
101760,
102401,
103040,
103042,
103685,
104977,
105626,
106277,
107585,
108242,
108899,
108901,
110225,
110593,
111557,
112226,
112895,
114245,
115601,
116963,
118335,
118337,
119026,
119717,
121103,
121105,
121802,
122501,
123905,
124999,
125315,
126737,
128165,
129599,
131045,
131071,
131073,
132497,
133955,
133957,
135425,
136901,
137642,
138383,
139875,
140609,
140626,
141377,
142885,
143642,
144401,
146688,
147457,
148224,
148878,
148997,
150545,
152101,
152882,
153665,
156815,
156817,
157463,
159202,
160001,
161605,
163217,
164026,
164837,
167282,
168101,
171395,
172226,
173057,
176399,
176401,
178085,
180626,
183185,
184901,
186623,
186625,
189226,
190097,
193601,
194482,
195113,
195365,
196250,
197135,
197137,
198026,
199808,
206117,
207937,
209765,
213443,
213445,
215297,
215999,
216001,
217157,
219023,
219025,
220901,
224677,
228485,
232325,
234257,
236195,
237168,
238145,
238327,
240101,
242065,
244037,
246017,
248003,
250048,
254017,
258065,
260099,
260101,
263168,
266257,
270401,
272483,
272485,
274624,
276677,
279935,
285157,
287297,
287497,
295937,
309137,
311365,
313601,
320357,
322623,
322625,
324899.
Some larger examples :
19642625,
19669226,
19704722,
19713601,
19731365,
19749137,
19758026,
19766917,
19784705,
19820303,
19820305,
19855937,
19873763,
19882682,
19891601,
19909445,
19936226,
19945157,
19963025,
19980901.