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admirable n.  and  centered pentagonal n.

First numbers that belong to both sets:

1266, 1626, 6126, 13506, 35106, 36906, 50766, 52926, 69306, 71826, 89776, 90726, 93606, 172266, 321306, 365766, 469806, 523266, 572406, 579606, 631266, 757626, 895506, 968766, 978126, 1205826, 1301406, 1378266, 1389426, 1574106, 1872726, 1978026, 2183226, 2197266, 2292016, 2296806, 2428026, 2532606, 2779926, 3038766, 3055326, 3189426, 3591006, 3884406, 4054506, 4505766, 4668306, 4854606, 5194806, 5369226, 5524206, 5546526, 5704026, 5726706, 6452106, 6646326, 6670806, 6843426, 7068606, 7452006, 7660626, 8050576, 8303766, 8523906, 8551626, 8746926, 9462426, 9697326, 10175766, 10634766, 11135526, 11390226, 11680206, 11908266, 11941026, 12171606, 12471306, 12706926, 12740766, 13013106, 13531506, 13566426, 14095626, 14131266, 14382006, 14671266, 16467306, 16815606, 17089026, 17443806, 18407706, 18693726, 18734766, 20370426, 20413266, 20757606, 21104826, 21411006, 21454926, 22522506, 23616006, 24312606, 24735426, 25448226, 26658726, 27797226, 27847266, 28198806, 29061726, 29833926, 29885766, 30668766, 30721326, 32427006, 32806266, 33681426, 34178766, 34623906, 35015766, 35071926, 35466306, 35919726, 35976606, 36433266, 36835206, 36892806, 37355226, 38230026, 39174306, 39710526, 40130106, 40612326, 42137826, 43128906, 43212016, 45145626, 45657006, 47143266, 47665806, 48719526, 50929206, 51472266, 52018206, 54720906, 56489406, 58141266, 58213626, 60479106, 60552906, 61665306, 61739826, 62362576, 62863026, 64072266, 64757526, 66525306, 67145766, 69735606, 70929006, 71008926, 72859506, 73590126, 74242626, 74898006, 77464806, 77548326, 78134226, 78890766, 79566306, 80159766, 81524526, 83593266, 87187326, 88610406, 89326266, 90045006, 91491126, 92948766, 96550026, 97390806.