First numbers that belong to both sets:
25,
121,
127,
128,
289,
625,
1022,
1024,
1255,
1296,
1395,
1435,
1503,
1792,
2048,
2187,
2500,
2503,
2504,
2507,
2509,
2592,
3159,
3685,
4088,
4096,
4106,
4167,
4624,
5776,
6145,
7928,
8092,
8192,
9025,
10192,
10201,
10251,
10368,
10426,
10525,
10824,
10935,
11163,
11259,
11264,
11439,
11663,
11665,
11943,
12006,
12100,
12103,
12104,
12107,
12109,
12167,
12337,
12493,
12505,
12544,
12550,
12595,
12769,
12843,
12960,
13125,
13286,
13496,
13689,
13725,
13764,
13822,
13825,
13826,
13832,
14035,
14175,
14641,
14647,
15003,
15030,
15246,
15379,
15568,
15613,
15621,
15622,
15625,
15626,
15628,
15631,
15633,
15634,
15645,
15655,
15656,
15661,
15662,
15667,
15679,
15688,
16225,
16245,
16295,
16348,
16372,
16375,
16381,
16382,
16384,
16387,
16447,
16479,
16743,
16758,
16783,
16797,
16798,
16807,
16879,
17253,
17368,
17384,
17482,
17536,
17856,
17892,
17920,
17925,
18225,
18270,
18594,
19321,
19453,
19592,
19653,
19682,
19684,
19693,
19734,
19737,
19738,
19773,
19845,
20736,
21175,
21375,
21495,
21504,
21606,
21753,
21844,
21848,
21870,
21875,
21953,
22264,
22528,
23326,
23392,
23456,
23546,
23548,
23796,
24336,
24339,
24367,
24375,
24389,
24390,
24393,
24564,
24584,
24964,
25105,
25314,
25375,
25725,
25872,
26348,
26624,
26754,
26896,
26973,
27889,
28217,
28226,
28547,
28554,
28556,
28559,
28561,
28564,
28672,
28678,
28749,
28764,
28900,
29282,
29517,
29523,
29525,
29526,
29529,
29584,
29632,
29929,
30625,
31250,
31252,
31256,
31346,
31509,
31682,
32744,
32747,
32761,
32762,
32764,
32768,
32771,
32778,
32783,
32785,
32786,
32795,
32825,
32836,
32845,
32851,
32853,
32854,
33579,
33655,
33696,
34968,
34992,
35152,
35684,
35721,
35932,
35942,
37249,
37814,
37840,
37845,
38416,
38912,
39283,
39295,
39313,
39314,
39342,
39356,
39362,
39368,
39382,
39456,
39864,
41468,
41472,
42875,
43268,
43688,
43691,
43932,
44676,
45056,
45361,
45362,
45364,
45367,
45368,
45632,
45864,
45947,
45978,
46256,
46615.
Some larger examples :
983041,
983042,
983044,
983047,
983048,
983445,
983485,
983750,
984150,
984375,
985768,
986947,
990025,
995336,
995341,
995344,
995347,
997246,
997375,
999964.