First numbers that belong to both sets:
25,
121,
127,
289,
347,
1022,
1255,
1285,
1296,
1435,
2349,
2500,
2501,
2503,
2592,
2916,
3159,
3375,
5120,
5832,
6144,
9261,
10255,
10525,
11259,
11264,
11665,
12101,
12106,
12107,
12109,
12321,
12337,
12493,
12505,
12798,
12955,
12960,
13225,
13689,
13813,
13822,
13823,
13825,
14035,
14129,
14175,
14647,
15125,
15435,
15567,
15586,
15617,
15623,
15627,
15629,
15632,
15633,
15634,
15635,
15641,
15661,
15667,
15679,
15689,
15795,
16295,
16347,
16375,
16381,
16382,
16387,
16447,
16448,
16743,
16759,
16765,
16879,
17437,
17482,
17536,
17689,
18432,
18522,
19453,
19629,
19653,
19693,
19739,
19773,
19845,
21504,
21843,
21943,
21953,
22528,
22757,
23456,
23552,
24375,
24385,
24964,
25105,
25375,
25725,
25895,
25921,
26624,
26896,
27436,
27648,
27653,
28547,
28559,
28674,
28749,
29160,
29184,
29517,
29519,
29527,
29531,
29584,
29632,
29768,
31509,
32765,
32771,
32783,
32785,
32795,
32815,
32845,
32855,
32875,
32885,
34993,
35152,
35933,
35937,
36457,
36864,
37187,
38912,
39304,
39313,
39343,
39424,
41323,
42025,
43264,
43375,
43691,
45056,
45361,
45367,
45369,
46613,
46615,
46619,
46633,
46643,
46649,
46663,
46691,
48751,
48757,
49277,
51200,
52493,
52731,
53248,
53824,
54432,
54872,
55225,
55296,
56875,
58921,
59051,
59053,
59057,
59129,
59263,
59273,
59319,
59392,
59759,
61440,
62503,
64513,
65491,
66339,
67149,
69255,
70225,
71199,
72576,
73984,
74353,
74358,
74897,
78163,
81648,
82944,
83357,
85264,
93217,
97336,
98375,
100255,
100525,
101299,
102384,
102464,
102497,
102528,
102595,
102783,
102784,
102955,
103681,
103685,
103687,
104329,
104366,
104448,
104816,
104879,
104895,
104897,
104969,
104978,
104979,
104986,
105025,
105250,
105295,
106289,
106929,
107329,
107632,
108233,
109351,
109353,
109355,
109357,
109358,
110758,
111132,
111536,
111630,
112505,
112640,
112895,
112896,
113724,
113725,
114245,
114291,
114377,
114647,
114674,
114679,
114696,
114737,
114779,
114921,
115249,
115699,
115934,
115968,
116317,
116342,
116478,
116625,
116635,
116827,
116837,
116937.
Some larger examples :
953321,
953341,
954368,
956497,
956587,
958693,
961375,
962361,
963272,
964859,
972197,
974848,
976553,
976559,
978121,
983750,
990025,
995341,
995347,
996543.