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Search a number
amenable n.  and  centered square n.

First numbers that belong to both sets:

1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325, 4513, 4705, 4901, 5101, 5305, 5513, 5725, 5941, 6161, 6385, 6613, 6845, 7081, 7321, 7565, 7813, 8065, 8321, 8581, 8845, 9113, 9385, 9661, 9941, 10225, 10513, 10805, 11101, 11401, 11705, 12013, 12325, 12641, 12961, 13285, 13613, 13945, 14281, 14621, 14965, 15313, 15665, 16021, 16381, 16745, 17113, 17485, 17861, 18241, 18625, 19013, 19405, 19801, 20201, 20605, 21013, 21425, 21841, 22261, 22685, 23113, 23545, 23981, 24421, 24865, 25313, 25765, 26221, 26681, 27145, 27613, 28085, 28561, 29041, 29525, 30013, 30505, 31001, 31501, 32005, 32513, 33025, 33541, 34061, 34585, 35113, 35645, 36181, 36721, 37265, 37813, 38365, 38921, 39481, 40045, 40613, 41185, 41761, 42341, 42925, 43513, 44105, 44701, 45301, 45905, 46513, 47125, 47741, 48361, 48985, 49613, 50245, 50881, 51521, 52165, 52813, 53465, 54121, 54781, 55445, 56113, 56785, 57461, 58141, 58825, 59513, 60205, 60901, 61601, 62305, 63013, 63725, 64441, 65161, 65885, 66613, 67345, 68081, 68821, 69565, 70313, 71065, 71821, 72581, 73345, 74113, 74885, 75661, 76441, 77225, 78013, 78805, 79601, 80401, 81205, 82013, 82825, 83641, 84461, 85285, 86113, 86945, 87781, 88621, 89465, 90313, 91165, 92021, 92881, 93745, 94613, 95485, 96361, 97241, 98125, 99013, 99905, 100801, 101701, 102605, 103513, 104425, 105341, 106261, 107185, 108113, 109045, 109981, 110921, 111865, 112813, 113765, 114721, 115681, 116645, 117613, 118585, 119561, 120541, 121525, 122513, 123505, 124501, 125501, 126505, 127513, 128525, 129541, 130561, 131585, 132613, 133645, 134681, 135721, 136765, 137813, 138865, 139921, 140981, 142045, 143113, 144185, 145261, 146341, 147425, 148513, 149605, 150701, 151801, 152905, 154013, 155125, 156241.

Some larger examples :