Search a number
economical n.  and  square n.

First numbers that belong to both sets:

1, 16, 25, 49, 64, 81, 121, 169, 256, 289, 361, 529, 625, 729, 841, 961, 1024, 1225, 1296, 1369, 1600, 1681, 1849, 2025, 2209, 2304, 2401, 2500, 2809, 2916, 3136, 3481, 3721, 3969, 4096, 4489, 5041, 5184, 5329, 5625, 6241, 6400, 6561, 6889, 7921, 9409, 9604, 10000, 10201, 10609, 10816, 11236, 11449, 11664, 11881, 12321, 12544, 12769, 13225, 13456, 13689, 13924, 14161, 14641, 14884, 15129, 15376, 15625, 16129, 16384, 16641, 17161, 17689, 17956, 18225, 18496, 18769, 19321, 19881, 20164, 20736, 21025, 21316, 21609, 21904, 22201, 22801, 23104, 23409, 24025, 24649, 24964, 25281, 25600, 25921, 26244, 26569, 26896, 27556, 27889, 28561, 29241, 29584, 29929, 30625, 30976, 31329, 31684, 32041, 32761, 33489, 33856, 34225, 35344, 35721, 36481, 36864, 37249, 37636, 38416, 38809, 39601, 40000, 40401, 41209, 42025, 42849, 43264, 44521, 44944, 45369, 46225, 46656, 47089, 47961, 49729, 50176, 50625, 51529, 52441, 53824, 54289, 55225, 55696, 56169, 57121, 58081, 58564, 59049, 59536, 60025, 61504, 62001, 62500, 63001, 65536, 66049, 67081, 68121, 69169, 70225, 71289, 71824, 72361, 73441, 73984, 75625, 76729, 77841, 78961, 80089, 80656, 82369, 82944, 83521, 84681, 85264, 85849, 87025, 87616, 88209, 90601, 92416, 93025, 94249, 96721, 97969, 99856, 100489, 101761, 102400, 103041, 104329, 104976, 105625, 106276, 106929, 107584, 108241, 109561, 110224, 110889, 111556, 112225, 112896, 113569, 114244, 114921, 116281, 117649, 118336, 119716, 120409, 121801, 122500, 123201, 123904, 124609, 126025, 126736, 128164, 128881, 129600, 130321, 131044, 131769, 133225, 134689, 135424, 136161, 137641, 139129, 140625, 141376, 142129, 142884, 143641, 145161, 145924, 146689, 147456, 148996, 149769, 150544, 151321, 152881, 153664, 154449, 155236, 156025, 157609, 158404, 160000, 160801, 162409, 163216, 164025, 165649, 167281, 168921, 169744, 170569, 172225, 173056, 173889, 175561, 177241, 178084, 178929, 179776, 180625, 182329, 183184, 185761, 186624, 187489, 190096, 190969, 192721, 194481.

Some larger examples :