First numbers that belong to both sets:
1,
8,
9,
16,
25,
32,
36,
49,
64,
81,
100,
121,
125,
128,
144,
169,
196,
216,
225,
256,
289,
324,
361,
400,
441,
484,
512,
529,
576,
625,
676,
729,
784,
841,
900,
961,
1000,
1024,
1089,
1156,
1225,
1296,
1369,
1444,
1521,
1600,
1681,
1728,
1764,
1849,
1936,
2025,
2048,
2116,
2197,
2209,
2304,
2401,
2500,
2601,
2704,
2744,
2809,
2916,
3025,
3125,
3136,
3249,
3364,
3481,
3600,
3721,
3844,
3969,
4096,
4225,
4356,
4489,
4624,
4761,
4900,
4913,
5041,
5184,
5329,
5476,
5625,
5776,
5832,
5929,
6084,
6241,
6400,
6561,
6724,
6889,
7056,
7225,
7396,
7569,
7744,
7776,
7921,
8000,
8100,
8192,
8281,
8464,
8649,
8836,
9025,
9216,
9261,
9409,
9604,
9801,
10000,
10201,
10404,
10609,
10648,
10816,
11025,
11236,
11449,
11664,
11881,
12100,
12321,
12544,
12769,
12996,
13225,
13456,
13689,
13824,
13924,
14161,
14400,
14641,
14884,
15129,
15376,
15625,
15876,
16129,
16384,
16641,
16900,
17161,
17424,
17576,
17689,
17956,
18225,
18496,
18769,
19044,
19321,
19600,
19881,
20164,
20449,
20736,
21025,
21316,
21609,
21904,
21952,
22201,
22500,
22801,
23104,
23409,
23716,
24025,
24336,
24389,
24649,
24964,
25281,
25600,
25921,
26244,
26569,
26896,
27000,
27225,
27556,
27889,
28224,
28561,
28900,
29241,
29584,
29929,
30276,
30625,
30976,
31329,
31684,
32041,
32400,
32761,
32768,
33124,
33489,
33856,
34225,
34596,
34969,
35344,
35721,
35937,
36100,
36481,
36864,
37249,
37636,
38025,
38416,
38809,
39204,
39304,
39601,
40000,
40401,
40804,
41209,
41616,
42025,
42436,
42849,
43264,
43681,
44100,
44521,
44944,
45369,
45796,
46225,
46656,
47089,
47524,
47961,
48400,
48841,
49284,
49729,
50176,
50625,
50653,
51076,
51529,
51984,
52441,
52900,
53361,
53824,
54289,
54756,
54872,
55225,
55696,
56169,
56644,
57121,
57600,
58081,
58564,
59049,
59536,
60025,
60516,
61009,
61504,
62001,
62500,
63001,
63504.
Some larger examples :
998812816,
998876025,
998939236,
999002449,
999065664,
999128881,
999192100,
999255321,
999318544,
999381769,
999444996,
999508225,
999571456,
999634689,
999697924,
999761161,
999824400,
999887641,
999950884,
1000000000.