First numbers that belong to both sets:
25,
121,
125,
127,
128,
153,
289,
343,
347,
625,
688,
1022,
1024,
1255,
1285,
1395,
1435,
1503,
1827,
2048,
2187,
2349,
2501,
2503,
2504,
2505,
2506,
2507,
2509,
2737,
3125,
3159,
3281,
3375,
3685,
4096,
4106,
4167,
4628,
6145,
6455,
7928,
8192,
9025,
9261,
10201,
10251,
10255,
10426,
10521,
10525,
10575,
10935,
11163,
11259,
11439,
11663,
11665,
11848,
11943,
12091,
12101,
12103,
12105,
12106,
12107,
12109,
12167,
12321,
12337,
12493,
12505,
12550,
12595,
12769,
12802,
12843,
12850,
12955,
13125,
13225,
13243,
13286,
13689,
13725,
13813,
13822,
13823,
13825,
13826,
14035,
14129,
14641,
14645,
14647,
15003,
15125,
15345,
15379,
15495,
15562,
15567,
15585,
15586,
15613,
15615,
15617,
15621,
15622,
15623,
15625,
15626,
15627,
15628,
15629,
15631,
15632,
15633,
15634,
15635,
15641,
15645,
15655,
15656,
15661,
15662,
15667,
15679,
15688,
15689,
15697,
15698,
15795,
15975,
16225,
16245,
16295,
16347,
16348,
16372,
16375,
16377,
16378,
16381,
16382,
16384,
16385,
16387,
16447,
16448,
16479,
16743,
16759,
16765,
16783,
16797,
16798,
16807,
16815,
16875,
16879,
17253,
17384,
17428,
17437,
17482,
17488,
17689,
17925,
18225,
18265,
18435,
18723,
19321,
19453,
19592,
19629,
19642,
19653,
19682,
19683,
19693,
19732,
19736,
19737,
19738,
19739,
19773,
20485,
21175,
21375,
21495,
21586,
21753,
21843,
21844,
21845,
21848,
21875,
21943,
21953,
22757,
23326,
23456,
23546,
24339,
24367,
24375,
24385,
24389,
24393,
24566,
24586,
24964,
25105,
25137,
25375,
25474,
25510,
25725,
25895,
25921,
26896,
26973,
27436,
27634,
27639,
27653,
27783,
27889,
28217,
28226,
28322,
28547,
28556,
28559,
28561,
28564,
28671,
28678,
28749,
29282,
29517,
29519,
29523,
29524,
29525,
29527,
29529,
29531,
29549,
29584,
29632,
29768,
29795,
29929,
30625,
31250,
31252,
31256,
31346,
31347,
31509,
31682,
32685,
32697,
32744,
32747,
32751,
32759,
32761,
32762,
32764,
32765,
32768,
32771,
32775,
32781,
32782,
32783.
Some larger examples :
983445,
983485,
983750,
984350,
985726,
986947,
989527,
990025,
995331,
995333,
995336,
995337,
995341,
995347,
995373,
995463,
996543,
997246,
997375,
999163.