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centered nonagonal n.  and  junction n.

First numbers that belong to both sets:

406, 820, 3916, 7021, 8515, 9316, 9730, 15931, 17020, 23005, 27028, 27730, 66430, 67528, 106030, 107416, 118828, 130816, 137026, 165025, 175528, 184528, 190036, 195625, 205120, 228826, 237016, 253828, 264628, 271216, 273430, 303031, 324415, 346528, 349030, 359128, 364231, 387640, 453628, 465130, 468028, 521731, 552826, 562330, 575128, 591328, 654940, 661825, 711028, 729028, 739936, 750925, 780625, 788140, 814726, 830116, 861328, 881128, 909226, 950131, 991936, 1000405, 1026028, 1047628, 1056331, 1095940, 1223830, 1228528, 1271215, 1314631, 1363726, 1423828, 1485226, 1574425, 1606528, 1633528, 1649836, 1666225, 1760626, 1910035, 2011015, 2065528, 2071630, 2096128, 2108431, 2303731, 2316628, 2342530, 2349028, 2534626, 2582128, 2616328, 2748340, 2762425, 2819125, 2862028, 2919736, 2941525, 3000025, 3066526, 3156328, 3194128, 3201715, 3224530, 3247426, 3324331, 3465028, 3504628, 3520531, 3592540, 3821230, 3837835, 3896236, 4065526, 4091230, 4117015, 4125628, 4273426, 4335040, 4352725, 4423825, 4522528, 4549636, 4732426, 4900015, 4975435, 5051431, 5224528, 5234230, 5273128, 5380840, 5509540, 5670028, 5935735, 6029128, 6081328, 6207526, 6281740, 6303025, 6453028, 6507028, 6539536, 6572125, 6681340, 7025626, 7344028, 7401628, 7529140, 7681240, 7811128, 7882435, 7966036, 8183035, 8207326, 8501626, 8613325, 8713225, 8750836, 9029125, 9054640, 9144226, 9480835, 9717436, 9983746, 10335331, 10362628, 10417330, 10431028, 10818226, 10860130, 10902115, 10916128, 11155726, 11283625, 11484028, 11556028, 11599336, 11642725, 11890126, 12066328, 12243826, 12647935, 12663028, 12905740, 13243231, 13274128, 13336030, 13351528, 13367035, 13475836, 13757635, 14106016, 14281840, 14313925, 14442625, 14491036, 14620528, 14669236, 14718025, 14881240, 15343030, 15727636, 15845635, 16134040, 16356340, 16511131, 16632028, 16649335, 16770736, 17084935, 17120026, 17243128, 17331328, 17704225, 17739946, 18045028, 18099136, 18153325, 18334540, 18902026, 19272736, 19422028, 19647046, 19722340, 19760041, 20177128, 20253430, 20272528, 20810926, 21043828, 21278026, 21454525, 21612025, 21730528, 21889036, 22107925, 22147840, 22710430, 22771126, 23177836, 23341528, 23362030, 23444128, 23670640, 24252130, 24273028, 24293935, 24819535, 25116328, 25372126, 25521940, 26038936, 26103925, 27221131, 27442936, 27621028, 27866845, 27889246, 28271440, 28520128, 28656235, 28815436, 29226835, 30361528, 30548836, 30619225, 30807325, 30854440, 31019626, 31114216, 31303828, 31422628, 31637035, 32044015, 32068036, 32260528, 32381128, 32647240, 32963140, 33231628.

Some larger examples :