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junction n.  and  nonagonal n.

First numbers that belong to both sets:

111, 204, 14625, 20026, 28125, 32016, 47619, 57024, 57921, 58825, 69231, 70219, 71214, 77331, 79426, 120621, 136719, 153825, 199326, 212914, 250714, 265926, 299739, 324825, 339924, 350919, 359841, 375724, 408519, 410914, 415725, 425431, 430326, 437721, 462826, 478225, 517825, 523224, 553419, 567424, 587325, 613416, 631125, 655129, 673426, 713934, 755625, 811929, 839125, 849439, 891325, 916224, 937839, 974424, 1023031, 1026819, 1030614, 1034416, 1061226, 1135725, 1151731, 1200421, 1204524, 1221006, 1250119, 1271124, 1365625, 1400829, 1468044, 1513729, 1546125, 1626229, 1664625, 1772524, 1848034, 1853124, 1863325, 1888950, 1919931, 1940725, 1961631, 1972126, 2025021, 2041026, 2051731, 2084014, 2094831, 2165824, 2426529, 2526625, 2568429, 2616625, 2770125, 2788839, 2864325, 3018321, 3024825, 3103419, 3123225, 3163026, 3183021, 3283941, 3290725, 3311119, 3317931, 3386436, 3393325, 3400221, 3476539, 3518524, 3732229, 3856125, 3870834, 3915129, 4049526, 4094829, 4155625, 4178539, 4201516, 4270825, 4395441, 4442634, 4450524, 4466325, 4650049, 4780041, 4911825, 4970044, 5020219, 5249125, 5317929, 5527029, 5544636, 5821125, 5848239, 6076639, 6159934, 6169224, 6197136, 6290631, 6300019, 6328225, 6337641, 6365931, 6508326, 6604131, 6710325, 6720021, 6797841, 7103625, 7183629, 7355125, 7375434, 7436529, 7446736, 7487634, 7508125, 7528644, 7797939, 7987146, 8200036, 8307531, 8350725, 8623225, 8667231, 8777736, 8811024, 8866644, 8888941, 8922439, 9238125, 9547734, 9617229, 9675334, 9721944, 10063216, 10254024, 10302006, 10314019, 10482936, 10604431, 10641016, 10653225, 10726626, 10763421, 10948341, 10960725, 11147325, 11297739, 11310319, 11373324, 11461825, 11652625, 11755029, 11832126, 11974125, 12143034, 12392029, 12776946, 12790324, 12870739, 12991834, 13005324, 13018821, 13181331, 13235725, 13290231, 13317526, 13454421, 13523131, 13688749, 13771936, 13813624, 13827534, 14135325, 14546226, 14703625, 14732334, 14804229, 14833036, 15079026, 15327039, 15503325, 15606624, 15769644, 15829134, 15844024, 15978349, 16053219, 16233621, 16415031, 16689036, 16704325, 16996146, 17540326, 17791950, 17807736, 17918434, 17950125, 17981844, 18220629, 18686746, 18848841, 18946434, 19240725, 19257141, 19306431, 19504221, 19636641, 20003106, 20120419, 20204424, 20576125, 20712129, 20968344, 21002625, 21140029, 21260625, 21450826, 21694125, 22079224, 22184839, 22361424, 22592031, 22663225, 22734531, 22770226, 22967049, 23002926, 23182731, 23417524, 24535044, 24572125, 24683536, 24739336, 24757950, 24813834, 24851125, 24888444, 25169229.

Some larger examples :