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centered octagonal n.  and  wasteful n.

First numbers that belong to both sets:

9, 225, 441, 1089, 1521, 2601, 3025, 3249, 4225, 4761, 5929, 7225, 7569, 8281, 8649, 9025, 9801, 11025, 20449, 27225, 34969, 38025, 43681, 48841, 53361, 61009, 64009, 65025, 74529, 81225, 89401, 91809, 95481, 99225, 119025, 127449, 148225, 159201, 184041, 189225, 207025, 216225, 233289, 245025, 308025, 314721, 342225, 354025, 370881, 378225, 393129, 416025, 423801, 439569, 442225, 480249, 497025, 511225, 549081, 576081, 585225, 603729, 632025, 648025, 670761, 680625, 731025, 741321, 783225, 804609, 815409, 837225, 874225, 915849, 938961, 950625, 974169, 1002001, 1046529, 1092025, 1221025, 1279161, 1334025, 1375929, 1461681, 1490841, 1525225, 1600225, 1656369, 1713481, 1718721, 1830609, 1863225, 2013561, 2082249, 2140369, 2187441, 2235025, 2295225, 2387025, 2393209, 2405601, 2499561, 2544025, 2556801, 2576025, 2608225, 2673225, 2732409, 2812329, 2832489, 2873025, 2907025, 2989441, 3059001, 3122289, 3136441, 3186225, 3359889, 3538161, 3553225, 3560769, 3629025, 3790809, 3822025, 3861225, 3956121, 3980025, 4004001, 4052169, 4060225, 4141225, 4223025, 4272489, 4347225, 4372281, 4380649, 4447881, 4498641, 4575321, 4601025, 4678569, 4774225, 4809249, 4888521, 4941729, 4986289, 4995225, 5049009, 5085025, 5112121, 5130225, 5184729, 5239521, 5294601, 5461569, 5489649, 5546025, 5593225, 5631129, 5659641, 5697769, 5745609, 5784025, 5803281, 5832225, 5909761, 5978025, 6007401, 6076225, 6275025, 6517809, 6682225, 6734025, 6796449, 6827769, 6943225, 6964321, 7102225, 7112889, 7177041, 7209225, 7241481, 7273809, 7306209, 7371225, 7382089, 7491169, 7502121, 7568001, 7590025, 7667361, 7812025, 7868025, 7958041, 8003241, 8105409, 8116801, 8208225, 8242641, 8277129, 8381025, 8450649, 8497225, 8520561, 8625969, 8673025, 8732025, 8803089, 8910225, 9018009, 9054081, 9126441, 9272025, 9333025, 9357481, 9418761, 9492561, 9678321, 9790641, 9828225, 9891025, 9966649.