First numbers that belong to both sets:
1,
9,
64,
121,
400,
5776,
6889,
7396,
8836,
9409,
10816,
12100,
17689,
18769,
27556,
29929,
30976,
33856,
34969,
37636,
49729,
65536,
69169,
69696,
70756,
75076,
75625,
76729,
80656,
110224,
124609,
126736,
132496,
134689,
156816,
162409,
165649,
190096,
196249,
206116,
208849,
215296,
254016,
284089,
286225,
298116,
344569,
388129,
389376,
390625,
401956,
405769,
414736,
427716,
452929,
458329,
467856,
484416,
497025,
508369,
509796,
512656,
524176,
525625,
528529,
582169,
599076,
617796,
646416,
657721,
664225,
665856,
695556,
715716,
734449,
746496,
767376,
799236,
822649,
853776,
868624,
876096,
893025,
937024,
968256,
970225,
978121,
1000000,
1020100,
1067089,
1075369,
1089936,
1136356,
1155625,
1175056,
1177225,
1179396,
1181569,
1199025,
1218816,
1285956,
1336336,
1352569,
1354896,
1357225,
1380625,
1382976,
1385329,
1401856,
1471369,
1481089,
1498176,
1527696,
1572516,
1605289,
1623076,
1648656,
1708249,
1726596,
1758276,
1803649,
1819801,
1838736,
1841449,
1909924,
1920996,
1940449,
1946025,
1971216,
2033476,
2053489,
2059225,
2062096,
2085136,
2090916,
2114116,
2178576,
2319529,
2325625,
2353156,
2356225,
2359296,
2362369,
2387025,
2399401,
2414916,
2474329,
2547216,
2576025,
2601769,
2604996,
2608225,
2611456,
2640625,
2643876,
2647129,
2686321,
2842596,
2859481,
2873025,
2890000,
2900209,
2903616,
2910436,
2927521,
2941225,
2944656,
2975625,
2989441,
3048516,
3087049,
3214849,
3265249,
3326976,
3370896,
3411409,
3437316,
3481956,
3489424,
3549456,
3553225,
3568321,
3575881,
3629025,
3663396,
3709476,
3779136,
3794704,
3825936,
3845521,
3900625,
3940225,
3944196,
4016016,
4092529,
4108729,
4186116,
4227136,
4264225,
4301476,
4305625,
4309776,
4313929,
4343056,
4363921,
4384836,
4562496,
4583881,
4691556,
4822416,
4862025,
4901796,
4919524,
4955076,
4963984,
4977361,
4995225,
5058001,
5067001,
5089536,
5094049,
5225796,
5267025,
5308416,
5363856,
5410276,
5447556,
5452225,
5470921,
5503716,
5546025,
5564881,
5645376,
5688225,
5798464,
5812921,
5909761,
5934096,
6115729,
6135529,
6240004,
6255001,
6275025,
6315169,
6325225,
6330256,
6380676,
6421156,
6446521,
6471936,
6579225,
6625476,
6697744,
6734025,
6760000,
6806881,
6817321,
6843456,
6890625,
6927424,
7049025,
7160976,
7187761,
7252249,
7257636,
7284601,
7295401,
7392961,
7463824,
7524049,
7535025,
7650756,
7661824,
7678441,
7750656,
7840000,
7890481,
7963684,
8088336,
8156736.
Some larger examples :
987593476,
987656329,
987719184,
988725136,
988913809,
989228304,
989605764,
991053361,
991305225,
991494144,
992880100,
993384324,
995276304,
995591809,
995781136,
996791184,
996854329,
996917476,
999065664,
999887641.