First numbers that belong to both sets:
1,
49,
1521,
4225,
7225,
8281,
11025,
12321,
14641,
15625,
22201,
24025,
27225,
27889,
28561,
42025,
45369,
54289,
59049,
64009,
70225,
73441,
75625,
76729,
83521,
105625,
106929,
108241,
123201,
126025,
127449,
140625,
143641,
156025,
157609,
164025,
170569,
178929,
180625,
185761,
190969,
196249,
207025,
227529,
239121,
241081,
251001,
263169,
269361,
277729,
292681,
294849,
332929,
337561,
354025,
356409,
398161,
408321,
413449,
416025,
423801,
429025,
461041,
502681,
519841,
522729,
528529,
531441,
570025,
588289,
707281,
727609,
737881,
801025,
808201,
889249,
896809,
908209,
958441,
962361,
966289,
1010025,
1050625,
1054729,
1096209,
1100401,
1138489,
1177225,
1199025,
1229881,
1234321,
1320201,
1329409,
1380625,
1385329,
1394761,
1447209,
1456849,
1471369,
1500625,
1575025,
1600225,
1682209,
1687401,
1734489,
1739761,
1836025,
1934881,
1974025,
2007889,
2024929,
2093809,
2099601,
2223081,
2229049,
2393209,
2399401,
2405601,
2411809,
2505889,
2518569,
2563201,
2569609,
2666689,
2772225,
2812329,
2819041,
2920681,
2934369,
2948089,
2961841,
2968729,
2982529,
2989441,
3003289,
3045025,
3066001,
3087049,
3108169,
3122289,
3150625,
3193369,
3352561,
3404025,
3426201,
3523129,
3560769,
3606201,
3659569,
3674889,
3829849,
3940225,
3996001,
4020025,
4084441,
4100625,
4173849,
4247721,
4447881,
4498641,
4507129,
4549689,
4575321,
4592449,
4601025,
4695889,
4721929,
4730625,
4782969,
4809249,
4844401,
4959529,
4968441,
4995225,
5040025,
5049009,
5094049,
5103081,
5130225,
5157441,
5166529,
5303809,
5349969,
5424241,
5452225,
5470921,
5489649,
5574321,
5755201,
5774409,
5803281,
5822569,
6155361,
6205081,
6245001,
6255001,
6285049,
6589489,
6671889,
6734025,
6827769,
6985449,
6996025,
7027801,
7038409,
7070281,
7198489,
7209225,
7295401,
7469289,
7756225,
7856809,
7958041,
8003241,
8025889,
8094025,
8116801,
8219689,
8346321,
8381025,
8427409,
8508889,
8543929,
8579041,
8814961,
8874441,
8934121,
8946081,
8958049,
9272025,
9296401,
9320809,
9504889,
9628609,
9728161,
9778129,
9803161,
9853321,
9966649.