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centered square n.  and  wasteful n.

First numbers that belong to both sets:

85, 221, 481, 545, 685, 925, 1105, 2665, 3281, 3445, 3961, 4141, 4325, 4901, 5305, 5513, 5725, 5941, 6161, 6385, 6613, 7565, 7813, 8065, 8321, 8845, 9113, 9385, 12325, 15665, 16745, 17113, 17485, 18241, 20605, 22261, 22685, 23545, 25313, 26221, 28085, 29041, 29525, 31001, 31501, 32005, 32513, 33025, 33541, 35113, 37265, 39481, 40613, 42341, 42925, 46513, 47125, 48361, 48985, 50245, 50881, 52165, 53465, 54781, 55445, 56785, 57461, 58141, 58825, 60205, 61601, 62305, 63013, 63725, 64441, 65161, 65885, 66613, 67345, 68081, 69565, 71065, 72581, 73345, 74113, 74885, 75661, 77225, 78013, 78805, 80401, 81205, 82825, 84461, 85285, 86945, 87781, 88621, 89465, 91165, 92021, 92881, 93745, 95485, 96361, 99905, 107185, 109045, 109981, 111865, 119561, 122513, 123505, 124501, 136765, 137813, 146341, 151801, 158485, 159613, 160745, 166465, 171113, 174641, 175825, 178205, 179401, 181805, 191581, 192821, 194065, 195313, 197821, 200345, 208013, 209305, 214513, 217141, 219785, 222445, 225121, 231881, 235985, 238741, 240125, 242905, 245701, 248513, 249925, 254185, 257045, 261365, 264265, 268645, 270113, 271585, 276025, 279005, 280501, 285013, 286525, 288041, 289561, 295681, 297221, 300313, 306545, 308113, 309685, 311261, 314425, 316013, 320801, 322405, 327241, 328861, 330485, 341965, 343621, 350285, 351961, 355325, 363805, 367225, 368941, 372385, 379321, 386321, 393385, 395161, 396941, 398725, 402305, 404101, 407705, 409513, 411325, 414961, 418613, 422281, 433381, 440861, 442741, 446513, 457925, 461761, 465613, 467545, 469481, 471421, 473365, 475313, 477265, 483145, 487085, 493025, 499001, 503005, 505013, 507025, 509041, 513085, 515113, 517145, 519181, 521221, 523265, 527365, 533545, 535613, 537685, 541841, 543925, 546013, 548105, 554405, 558625, 560741, 562861, 564985, 567113, 569245, 573521, 575665, 577813, 579965, 582121, 586445, 588613, 590785, 597325, 601705, 606101, 608305, 610513, 612725, 614941, 619385, 621613, 623845, 626081, 628321, 630565, 635065, 639581, 641845, 644113, 646385, 648661, 650941, 653225, 655513, 657805, 660101, 664705, 669325, 671641, 676285, 678613, 680945.

Some larger examples :