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centered octagonal n.  and  tau n.

First numbers that belong to both sets:

1, 9, 225, 441, 625, 1089, 1521, 2025, 2601, 3249, 4761, 5625, 6561, 7569, 8649, 12321, 15129, 16641, 19881, 25281, 31329, 33489, 35721, 40401, 45369, 47961, 50625, 56169, 62001, 71289, 84681, 91809, 95481, 99225, 103041, 106929, 114921, 117649, 145161, 154449, 164025, 168921, 173889, 199809, 205209, 221841, 239121, 245025, 251001, 269361, 275625, 288369, 294849, 321489, 328329, 335241, 342225, 349281, 356409, 400689, 447561, 463761, 471969, 488601, 514089, 522729, 540225, 567009, 585225, 594441, 622521, 651249, 660969, 680625, 690561, 710649, 720801, 731025, 772641, 793881, 848241, 870489, 881721, 893025, 904401, 950625, 986049, 1022121, 1058841, 1071225, 1083681, 1096209, 1108809, 1121481, 1159929, 1212201, 1252161, 1292769, 1320201, 1361889, 1418481, 1447209, 1500625, 1505529, 1580049, 1595169, 1625625, 1671849, 1687401, 1703025, 1734489, 1766241, 1814409, 1879641, 1896129, 1912689, 1929321, 1946025, 1962801, 2030625, 2064969, 2134521, 2169729, 2241009, 2277081, 2331729, 2368521, 2442969, 2461761, 2480625, 2634129, 2692881, 2772225, 2792241, 2852721, 2913849, 2934369, 2975625, 2996361, 3101121, 3164841, 3229209, 3250809, 3294225, 3316041, 3381921, 3404025, 3426201, 3448449, 3470769, 3583449, 3697929, 3721041, 3744225, 3767481, 3837681, 3908529, 3932289, 4076361, 4100625, 4124961, 4198401, 4297329, 4322241, 4422609, 4473225, 4524129, 4652649, 4730625, 4756761, 4835601, 4862025, 4915089, 4968441, 5076009, 5157441, 5212089, 5322249, 5377761, 5405625, 5517801, 5574321, 5688225, 5716881, 5890329, 5919489, 6036849, 6066369, 6095961, 6125625, 6155361, 6185169, 6305121, 6335289, 6426225, 6548481, 6610041, 6640929, 6702921, 6890625, 6922161, 6985449, 7017201, 7049025, 7080921, 7144929, 7403841, 7469289, 7535025, 7601049, 7700625, 7767369, 7901721, 7969329, 8037225, 8071281, 8173881, 8415801, 8485569, 8555625, 8590761, 8696601, 8838729, 8946081, 8982009, 9090225, 9150625, 9162729, 9235521, 9345249, 9381969, 9455625, 9566649, 9603801, 9715689, 9903609, 9941409, 10131489, 10169721, 10208025, 10284849, 10323369, 10400625, 10634121, 10712529, 10751841, 10791225, 10830681, 10949481, 11029041, 11068929, 11229201, 11350161, 11471769, 11923209, 11964681, 12006225, 12131289, 12173121, 12341169, 12425625, 12552849, 12638025, 12680721, 12809241, 12895281, 12981609, 13242321, 13329801, 13461561, 13505625, 13593969, 13638249, 13771521, 13950225, 14040009, 14265729, 14493249, 14630625, 14676561.

Some larger examples :